The two nations have tabled a blueprint for closer integration among willing member states, which includes a new membership “even for the UK”, according to reports.
Lord Heseltine told The Independent the UK must urgently explore the idea as the “over-arching majority of people in Britain see Brexit as a mistake”.
The Labour leader said the meeting began with an “exchange of gifts” and covered topics including “the relationship between our two countries” and future “prosperity and security”.
Sir Keir stressed plans to build on the relationship between France and Britain if Labour wins power.
As part of the proposals put forward by France and Germany, an “associate outside tier” of European countries would be created.
These counties would not be “bound to ‘ever closer union’,” the plans state, but could choose a “permanent frictionless trade relationship” with the bloc, The Times reported.
A European diplomatic source told the paper it was designed with Labour in mind, despite Sir Keir having ruled out rejoining the EU’s single market.
“It is carefully balanced politically to be a potential place for Britain without the need to ever rejoin the EU or to hold a referendum,” they said.
And associate membership would not include a customs union with the EU, allowing Britain to keep an independent trade policy.
Lord Heseltine said: “The remorseless pressure of public opinion is changing the dynamic of politics.
“The dam is breaking and there is increasingly a move towards integrating with Europe. This is an opportunity offered by France and Germany which should be seized upon.
“The overarching majority of people in Britain see Brexit as a mistake even those who still believe in it agree it has never been possible to implement it.”
The Tory former deputy prime minister went on: “The Tories have at least recognised change is needed, firstly with Northern Ireland and the Windsor Agreement and then with Horizon, allowing cooperation on sciences and technology.
“While the Red Wall may be insurmountable on this side of the General Election, the pressure of events will push people of both main parties to dare to change and to make permanent links with Europe.
“This new plan between France and Germany must be explored urgently.”