The classic time is over," declares restaurateur Maxime Alary in throaty, French-accented English. He's one of the three brothers behind modern French restaurant Blanchette and its recently opened sister, Blanchette East. "There's a new wave of French bistro."

Bold words indeed, but they're not without substance. 2016 has seen a glut of new French restaurants opening up in London, yet each one is definitely a significant departure from the classic haute cuisine that has long dominated the city's French food scene.

A roll call will inevitably mention the likes of Pierre Koffmann, whose influence on our food culture saw him receive the Lifetime Achievement award at this year's AA Hospitality Awards; Hélène Darroze and her two Michelin-starred restaurant at The Connaught hotel; and Michel Roux Jr and his iconic Mayfair restaurant Le Gavroche, among others.

These bastions of French cooking are undeniably among the best chefs in the world, but the food they serve, and the atmosphere in their restaurants, is almost uniformly fine dining. "The traditional French restaurant is not very relaxed. The waiters are all formally dressed and the menu is set out in a certain way," says Alex Jackson, whose recently opened neighbourhood joint Sardine on Old Street specialises in food from southern French regions, including Provence and Languedoc. "I don't really think of French food as being a big part of what I eat in London, which is funny because I love it. It's just been a bit boring here."

Ali Burgess, who runs Petit Pois on Hoxton Square, agrees that the traditional French fine-dining restaurant isn't as highly regarded as it once was: "The whole point of French cuisine originally was home-cooked food, and they would cook it for everyone. It all got a little bit too serious – I think that's why people fell out of love with it, and why it fell by the wayside."

People don't talk about Paris influencing London's food any more

Jackson shares this opinion: "People don't really talk about Paris influencing London's food any more, which is really interesting." It's worth mentioning that both Burgess and Jackson are British – so when they talk about French cuisine, it's from a different perspective to the French restaurateurs who have come to London and set up bistros that are based on the food that they know from home.

In a city that's constantly hungry for new trends and that's known for its exacting standards, French cooking – no matter how good it was – seemed to lose its edge. But this new wave is reminding us just why it was so highly prized in the first place.

Whether it's a modern, marble-tiled brasserie on Henrietta Street in Covent Garden or a pocket-sized bistro in Bermondsey that seems straight out of Lyon, London's French restaurants are reintroducing us to a cuisine that focuses on great produce that's cooked really well, rather than with complicated techniques, and a style of dining that's casual, intimate and reasonably priced enough so that we can, and do, keep coming back.

This is a feeling shared by London's French restaurateurs. Blanchette's Alary tells me, with palpable excitement, that "French food is making a comeback. London is so full of culture that it has an open mind to French food with a modern twist."

Alary and his brothers run Blanchette and Blanchette East, which both specialise in classic French dishes, but served with a contemporary flourish on tapas-style sharing plates and, like Sardine, with influences from the south. "When we opened our first restaurant in Soho, we were worried about people being tired of classic French dishes so we wanted to bring modernity," he says.

"At Blanchette East, we're bringing a little bit more spice into it. We're using some new spices from the North Africa and the South of France." The result is a menu that reflects the influence of Moroccan and Tunisian cooking, with a signature dish of lamb tagine, a melt-in-the-mouth concoction that's rich in flavour and studded with dried apricots.

Gregory Marchand, chef-owner of Covent Garden's Frenchie, agrees with Alary's emphasis on the importance of new cultural influences. "I think a lot of young French chefs have been travelling and coming back with new ideas. At Frenchie, I created a place I'd like to go myself based on my travels.

"A lot of things are evolving very, very fast," he says. "I think that French cuisine at one point wasn't taking part of this change, but today it definitely is."

Marchand has been a key player in the development of the modern French bistro in Paris, where the 'bistronomy' movement has seen top chefs focusing on informal offerings with great food rather than coveting Michelin stars. Frenchie Covent Garden is the London outpost of his stable of Parisian restaurants of the same name – Frenchie, Frenchie Bar à Vins, and Frenchie To Go, which dishes up reuben sandwiches and other quick bites that are ideal for eating on the hoof. The Henrietta Street site, decked out in marble and sleek art deco lighting, epitomises the idea of a modern brasserie – yet it remains a world away from the stiff, outdated French restaurants of old, in both its cooking and its attitude.

Frenchie's food is French, yes, but there are many other influences visible on its menu. There's pappardelle, the broad, flat pasta that Marchand fell in love with while working in Italy; there are irresistibly moreish bacon scones; there's Cornish turbot with tomato, figs, muscat grapes and tarragon; and to celebrate our game season, there's Lincolnshire grouse with beetroot, blackberries and hay. The menu may take its lead from French traditions, but Marchand has woven together produce and techniques he learned about while travelling to create a menu that spans several cuisines.

There's so much to France and the breadth of the food is incredible

Equally important is that modern French food finally looks beyond Paris. Sardine is run by chef-patron Alex Jackson, who earned his stripes under Stevie Parle at Dock Kitchen, and focuses on food from the South of France. "There's so much more to France and the breadth of the food is incredible. You didn't really ever see it in London and you didn't really see it in Paris," he says.

"What I'm interested in is Southern French food. That sweep down from Catalunya to the whole Riviera. There's just so much going on," Jackson tells me over a plate of deliciously ripe figs and mozzarella so creamy it's close to collapse – a simple dish that's as Italian as it is French. "There are influences from North Africa; further south west there's paella and bull fights; and then in the south of France pâtes au pistou is pasta with pesto, and it's just as authentic there as it is in Liguria."

Sardine's menu reflects these Mediterranean influences, but still remains undeniably Français: lamb à la ficelle (similar to a spit roast); girolle mushrooms with grilled polenta; onion and anchovy tart; saucisse seche. As Jackson points out, "a lot of the food here doesn't tick the boxes of what to put on a French menu but it's more about an attitude, a spirit. I'm perfectly happy putting figs on a plate. It's not showing off my technical ability, but that's not the point."

Frenchie's tortellini

Frenchie's tortellini

And this, ultimately, is what is all boils down to: creating French food that's free from fuss and formality. Petit Pois sits above – and is owned by the same people as – Happiness Forgets, the cocktail bar that recently clocked in at number ten on the World's 50 Best Bars list. Here, French cooking has not been 'modernised'. Instead, it's the classics, but done extremely well: you'll find sole meunière, steak frites, and a chocolate mousse that's already garnering a following for its sheer size as well as its flavour and texture. Founder Ali Burgess is frank about the menu's aims: "What we would love is to bring French cooking back and just make food for the people."

Elsewhere, Bermondsey Street's Casse Croute similarly focuses on this traditional style of eating, served in a 25-cover restaurant that feels as if it's been there since the 1950s. "Our food is comfort food," says owner Hervé Durochat. "It's something that maybe you can eat at home but you don't necessarily need or want to do it, so you come to Casse Croute, where you can have the entertainment and the atmosphere." The food here is as French as it can possibly get: the menu changes every single day, with three starters, three mains and two desserts. "My chef is recreating dishes from his books when he was at school when he was 18. He's now 43."

This authentic feel permeates everything from the décor to the food and the service. Diners are greeted in French and the menu is written in French – "A lot of people come through the door and feel like they're in Paris or Lyon. That was our little goal."

Whether London's French food offering focuses on modern dishes or on the classics, as Marchand reminds me, "French cooking is still the base for most of the cuisines in the world." He believes instead that "it's actually more the attitude as a whole and the ambience which is changing."

"The culture about French food being snotty, that's all changing," he continues. "Service in London has been a bit more polished. There's been a switch. Restaurants have realised that the service needs to be a little less frightening for customers. People go out to have fun." London's French restaurants have long been associated with a bit of polish; formal service that features starched white tablecloths and fawning waiters – and this is precisely what we've moved away from.

It's about creating food that's free from formality

This departure is seeing a return to more intimate establishments. Familiarity is key – at Blanchette, "my brothers and I try to spend the maximum time in our restaurant. Taking orders, delivering food, being there at the entrance to greet guests or working behind the bar," says Alary. "You get to know the owner and you feel that you're being looked after better." Similarly, Durochat at Casse Croute and Burgess at Petit Pois spend much of their time working front-of-house and interacting with their clientele.

"The French bistro is a place where you feel at home, it's very cosy, it's something you want to go back again and again," says Blanchette's Alary. And this is how these restaurants are staying full every night. "60% of our clientele are regulars. It's always the same people." Frenchie's Marchand echoes Alary's words: "That's our strength here. This is how we fill our restaurants all the time, getting people to come back."

Each of these restaurateurs has a slightly different take on French dining – and that's perhaps what is most striking. They've all identified what it is specifically that they love about it, whether it's creating an intimate ambience, serving classic dishes that are cooked to absolute perfection, or celebrating regional cuisine that's often overlooked, to remind us exactly what made French cooking great. Characteristics, it seems, that Londoners still find irresistible.