The route would make use of the new high-speed railway linking Tours and Bordeaux.
Four railway line owners are involved: HS1 Ltd (Kent to London), Eurotunnel, SNCF-Réseau (Calais to Tours), and Lisea (new line Tours to Bordeaux).
They are talking to several international companies – not only Eurostar – about operating the new service.
Edmund Butcher, business development manager for HS1 Ltd, said discussions were going well.
The four companies met in January and will meet again in April to discuss developing an international station at Bordeaux-Saint-Jean.
Mr Butcher said: “The advantage with the train over the plane is that you only have to show your passport once at the start of the journey, but for that we would need to introduce a border control at Bordeaux. The trains would go through to St Pancras, where the necessary systems are already in place.”
He said Brexit will not change passport control requirements and does not threaten the proposed service.
The four companies are convinced the service will be popular.
Mr Butcher said: “It will take you straight into the heart of London, it will be comfortable, you will be able to work with internet connections and you can take your baggage without extra cost.
“Prices will be competitive at an average €89 for a one-way ticket.
“Our studies show that one in four British citizens living in France live in the Nouvelle Aquitaine region and in 2017 over one million flew between the region and London.
“We are convinced many of them will choose a direct train line if it is on offer as nine out of 10 travelling between Paris and London have already made this choice.” There would be no need to change stations in Paris as the route skirts around the city.
A new Bordeaux-Brussels link has also been confirmed.
It comes as a new report on the Paris-Bordeaux high-speed train line shows that 25% of traffic now comes from SNCF’s low-cost TGV service, Ouigo.
Passenger numbers have beaten predictions (3.7million in 2018 compared to 3.5million estimated).
It is 18 months since the line was launched, offering journey times of just two hours and four minutes between Bordeaux and Paris.
TGV use in France has grown by 15% over the same time, SNCF said.
“No frills” Ouigo launched in 2017 with tickets starting at €16 per journey. The average cost of a return between Paris and Bordeaux is €85.
SNCF now plans to launch four million Paris-Bordeaux return tickets for €39.