While there is large agreement on the questions of immigration and defence, the two are still at odds over eurozone issues.

Here's an outline of the various reform proposals for a post-Brexit Europe.

- Migration -

A record influx of migrants, many fleeing war in Syria and Iraq, has become a defining issue for politics in many EU nations.

Merkel is facing down a domestic rebellion over her liberal policy that led to the arrival of more than a million asylum seekers since 2015, while Italy last week sparked an outcry by refusing aid ships carrying rescued migrants to dock in its ports.

Paris and Berlin agree that there must be standard rules on asylum seekers across the bloc. They also subscribe to the idea of creating an European office on immigration, as well as a European border force.

A plan to reform the so-called Dublin rules, which require the country where migrants first arrive to deal with their asylum requests, is still being fine-tuned.

Merkel and Macron both agree that the current rules put disproportionate pressure on countries on the southern fringes of the EU, like Italy and Greece.

The German leader had initially championed a quota system to distribute migrants across the bloc, but this has been torpedoed by several central European nations.

She is now seeking to win support with the idea of a "flexible solidarity system, where countries contribute in different ways and means.

Macron's approach is a monetary incentive system encouraging countries to take in migrants.

- Eurozone -

Macron's ambitious ideas for a eurozone finance minister or parliament have been shot down by Berlin.

But Merkel has offered a concession in the form of an investment budget for the bloc, even though the amount she is willing to stump up is far less than what France is seeking.

For Merkel, the total sum should be "at the lower end of the double-digit billions of euros range", but Macron wants several hundred billion.

Macron has suggested that this could be financed by a tax on financial transactions.

Beyond that, in order to better cope with future crises, a deal is being drawn up on expanding the remit of the current European Stability Mechanism (ESM).

While it is currently the firefighter for eurozone countries with serious debt problems, there are visions for the ESM to evolve into a European version of the International Monetary Fund.

This could include expanding its powers to provide loans to countries that are victims of crises not linked to their debt levels.

The idea of naming it the European Monetary Fund has however been dropped at the request of France which did not want it to overshadow the IMF, according to Spiegel weekly.

Paris also wants to complete banking union with a system of guarantees for deposits in the eurozone in case of a financial crisis.

But Germany believes that it should be up to the banks to clean up their balance sheets instead of leaning on a state guarantee.

- Common defence -

In the face of US President Donald Trump's "America First" policy, a traditionally pacifist and atlanticist post-war Germany has drawn closer to France's call for a sovereign Europe, including in the military aspect.

Merkel backs Macron's idea for an European intervention initiative, with armies to collaborate before eventually forming a common force.

But France wants this force outside the framework of the EU, to allow Britain to join in even after it leaves the bloc.

Germany prefers it to remain within the EU.

- European bureaucracy -

Germany and France are in agreement about reducing the size of the European Commission, even if that means temporarily giving up on the idea of a rotating system for various commissioners.

Merkel has made a gesture towards Macron by agreeing to create a transnational list for European elections, on which there could be candidates for leading jobs at the European executive.