Meeting before a summit dinner of EU leaders in Estonia, Mrs Merkel and the recently elected Mr Macron are keen for the bloc’s founders to drive it forward in the wake of Brexit, though the losses she suffered in winning a fourth term on Sunday mean Europe’s leading politician faces uncertain support at home.
On Tuesday, Mr Macron outlined bold proposals for a European renewal, calling for the European Union to work more closely on defence and migration and for a euro zone budget.
He urged his peers to put European vision above national interests, saying in his address that he had “no red lines, only horizons”.
However, he faced a cautious hearing when he expounded his ideas to fellow EU leaders over dinner in Tallinn.
Lithuania’s no-nonsense President Dalia Grybauskaite tweeted while the discussion were ongoing: “European horizons drawn. “Important to avoid mirages in the desert on the way.”

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The informal get-together was arranged on the fly before a “digital summit” on issues ranging from data and cybersecurity to raising more tax from online firms.
It had no set agenda and could range widely, even allowing for Prime Minister Theresa May to pitch her ideas on Britain’s looming exit from the European Union. But diplomats said its focus will be on the fizz of new initiatives, notably from Mr Macron.
An EU source said there was a “strong and shared willingness to maintain the unity” and that the European Union should be “open to address new ideas” while continuing to work to deliver concrete results for citizens.
A French presidential source said France was not trying to impose its ideas on its partners but to show them that they were in their common interest and recognised that some needed time to reflect.
“The idea is not about forcing people to give a binary response. France cannot force things,” the source said, adding that Paris hoped leaders could agree on a way to work on the ideas in the coming weeks before an October summit in Brussels.
The Estonia meeting comes four days after a German election that has raised the prospect of months of tough coalition talks for Mrs Merkel, the most influential EU leader, and two days after Mr Macron’s rallying cry for deeper integration of national economies.
“Macron has stolen the show,” one senior EU official said of the dinner debate.
Many admire the youthful new French president’s energy and oratory after years in which Paris, long a driving force of the European Union, has appeared bereft of self-confidence.
Mrs Merkel told reporters before a meeting with Mr Macron that his ideas could be the basis for “intense” Franco-German cooperation.
She said: ”As far as the proposals were concerned, there was a high level of agreement between German and France.
“We must still discuss the details, but I am of the firm conviction that Europe can’t just stay still but must continue to develop.”
However, she may find it hard to commit Berlin to much as she has barely started the process of building what is likely to be a three-way coalition government.
Mr Macron was also likely to face polite but firm resistance at the dinner to his calls for a substantial pooling of national budgets in the euro zone and a possible breakaway by the wealthy, western states into a deeper monetary union.
The French presidential source recognised that eurozone matters would not be easy and that it might not be possible to have agreement on all items, although Mrs Merkel had not ruled anything out.
Eastern European leaders are cautious about the risk of new cleavages on the continent leaving them behind, while there are plenty, like Dutch Prime Minister Mark Rutte, a moving spirit behind the Tallinn dinner, who are sceptical about more financial burden-sharing before southern neighbours – including France – put their own national budgets on a sounder footing.