By Sarah Marsh and Andreas Rinke

BERLIN (Reuters) - France and Germany's governments kick off an unprecedented two-day retreat in Hamburg on Monday in a bid to re-set relations between the European Union's two biggest powers amid a host of disagreements on energy, industry and defence policy.

The French-German motor that has driven EU policy for decades has proven rusty of late although it is more necessary than ever given the multitude of crises the bloc faces, say analysts and lawmakers.

Europe is grappling with surging irregular migration, the transition to a carbon neutral economy, the Ukraine war, a shift in the relationship with top trade partner China and now also conflict in the Middle East.

"The Franco-German relationship, and as a result Europe, is not living up to the challenges we are currently facing," said Jacob Ross at the German Council on Foreign Relations.

One of the problems is that French President Emmanuel Macron sees himself as the natural successor to former Chancellor Angela Merkel as leader of Europe, and has adopted strong stances in Brussels, some contrary to German interests, he said.

On the German side, the Russian invasion of Ukraine has led Berlin to focus more on its transatlantic alliance with its top security partner, the United States - possibly at the cost of its relationship with France.

A lack of chemistry between the charismatic Macron and tight-lipped German Chancellor Olaf Scholz has also made it more difficult also for both governments to hammer out their differences, say lawmakers and diplomats.

"Macron and Scholz are simply very different personalities," Anton Hofreiter, chair of the German parliament's Committee on European Union Affairs and member of the Greens.

The two countries' current major point of contention is EU electricity reform, with Germany and some other EU states pushing for stricter rules on state-backed support of power prices that would hurt French industry.

Both governments play down their differences in public.

"Ultimately the point of bilateral relations is to overcome differences- that is the core of the EU," a French cabinet member said, on condition of anonymity.

The two-day retreat in the northern port city of Hamburg, where Scholz was mayor from 2011 to 2018, aims to put the relationship on a new footing rather than to yield concrete policy initiatives.

The informal team-building exercise is in keeping with the German tradition of holding cabinet "Klausur" or retreats.

The stakes are high, said Detlef Seif, a leading German Christian Democratic Union lawmaker on EU affairs.

"If both decide to just pursue their own interests, then not only will both lose out but so will the EU, which is not as strong and stable as it should be," he told Reuters.