Hollande is pushing for European authorities to adopt common measures to prevent costly bank failures and to directly recapitalize lenders in difficulty.
Having won backing for that from Italy's Prime Minister Enrico Letta last week, Hollande is now looking to bring Spanish premier Mariano Rajoy on board, French officials said.
The push for closer EU banking supervision was largely driven by Spain's woes last year, when it was forced to accept an emergency credit line from its eurozone partners to save its financial sector from collapse.
Hollande is expected to reiterate his call for European Union countries "to make jobs growth and stability the heart of their decisions" at their summit next month.
France and Spain will also discuss economic growth at their summit on Wednesday, with Hollande looking for support to boost investment capacity and pro-growth policies across the eurozone, officials said.
Growth is a major concern for Spain, the eurozone's fourth-biggest economy, which has just crawled timidly out of two years of recession with 0.1 percent growth in the third quarter of this year.
The summit in Madrid will discuss France's proposal for an "economic government" of the eurozone with a permanent Eurogroup chairman to oversee members' economic policies.
It will also address unemployment, which in Spain is painfully high at nearly 26 percent and more than 54 percent among the under-25s. French officials said Madrid was pushing for an efficient use of European resources to combat youth joblessness.
Other issues on the agenda of the summit, which involves various ministers from both countries, are migration, defence, anti-terrorism measures and transport.
A new high-speed railway from Paris to Barcelona is due to be opened in mid-December. Officials say it will cut the non-stop train journey time between the two cities to six hours and 20 minutes.
Hollande, Rajoy and their ministers were due to have lunch together at 1315 GMT before the summit proper and to give a joint press conference afterwards at 1715 GMT.