French President Emmanuel Macron has welcomed Angela Merkel's election victory but he may have difficulties selling his European reform agenda to whatever coalition she manages to cobble together.

Macron was quick to congratulate his German counterpart on winning a fourth term in Sunday's election, promising that the two key European partners would keep up their "essential cooperation".

Merkel's Christian Union CDU/CSU bloc scored 33 percent, but her victory was bittersweet, as the anti-immigrant Alternative for Germany (AfD) surged to become the country's third strongest party.

Merkel's conservatives dropped more than two million votes in the first national election since she opened Germany's doors to more than one million mostly Muslim migrants, many from war-torn Syria.

Her score puts her -- and also potentially Macron -- in a difficult position as she gets down to coalition talks, expected to be with the pro-business Free Democrats (FDP) and the left-leaning Greens.

The consultations could take months and grind Macron's hopes for a shake-up of the eurozone to a halt, putting strain on the EU's power couple.

- 'Cash pipeline' -

FDP leader Christian Lindner has already poured cold water on some of Macron's proposals for reforming the European Union, including giving the eurozone its own budget and finance minister -- an idea Merkel has cautiously greeted.

"If the idea of giving the eurozone its own budget is for a cash pipeline out of Germany to other European states, we won't help make it happen," Lindner told a rally days before the election.

"A transfer union like that wouldn't strengthen Europe, but weaken it," said Lindner, who has been sharply critical of the bailouts that have kept Greece in the euro.

"If she allies with the liberals, I'm dead," Le Monde newspaper recently quoted Macron as telling a visitor to the Elysee Palace.

Since his election in May on a passionately europhile platform Macron has gone out of his way to build ties with Merkel, visiting Berlin on his first foreign trip and rushing through labour reforms he sees as key to restoring credibility with Berlin.

On Tuesday, he will set out his EU reform proposals in a speech at the Sorbonne university in Paris.

French Prime Minister Edouard Philippe travelled to Berlin on September 15 to try to nail down Merkel's support for Macron's proposals, which also include giving the eurozone its own parliament.

But while agreeing for the need to "strengthen eurozone governance" Merkel used Philippe's visit to warn of the need to "back up the vocabulary used... with content".

- 'Cart before the horse' -

The German government is particularly wary about Macron's proposal for a eurozone budget amounting to several percentage points of the bloc's GDP that would principally benefit weaker members.

Berlin estimates that this could amount to up to 300 billion euros, of which Germany -- the eurozone's biggest economy and chief bailout bankroller -- would have to pay the lion's share.

Macron's idea of the eurozone being able to borrow money collectively is also acutely sensitive in Germany.

"The debate launched by the French president is being followed with some exasperation in the chancellor's office," the conservative Frankfurter Allgemeine Zeitung daily wrote at the weekend.

"He talks about solutions before the question has even been properly discussed," the paper added, accusing him of "putting the cart before the horse".

Merkel is nonetheless been keen to support her reform-minded French counterpart in the face of rising populism -- a fact that could be accentuated by the rise of the AfD.

"There is a very strong realisation in Germany, in particular in Mrs Merkel's party, of the urgent need to do something," Helene Miard-Delacroix, a historian specialising in Franco-German relations at the Sorbonne, told AFP recently.

Merkel herself told Philippe she has "no doubt we will found common solutions with France".

Source: AFP