Hollande flew to Madrid at a difficult moment, with France's economy shrinking 0.1 percent in the third quarter and a poll this month showing only 21 percent of the French approved of his policies, the lowest rating since the presidential system began more than 50 years ago.
The Socialist French leader, accompanied by his Prime Minister Jean-Marc Ayrault and eight ministers, can expect to find support from Spain's conservative Prime Minister Mariano Rajoy for reforms to how the eurozone operates at a December 19-20 European Union summit.
The French president, who was booed at a Remembrance Day ceremony in Paris this month, will find a warmer reception in Madrid where his team will have a working lunch with their hosts before a summit and a joint news conference with Rajoy.
Despite objections in Germany, Hollande and Rajoy both advocate creating a single banking authority capable of directly bailing out a member country's troubled banks, without asking the host state to foot the bill and thus push up its sovereign debt.
A French presidential official said it was the plight of Spain that sparked the original banking union proposal in June 2012, when the country faced being "trapped in a negative spiral" of rising sovereign debt and larger banking rescues.
Spain's eurozone partners last summer agreed to extend a banking rescue loan of up to 100 billion euros to shore up shaky Spanish institutions laden with weak assets since the collapse of a decade-long property bubble in 2008.
Madrid ended up using just 41 billion euros of the money for a bank restructuring programme, which ends in January, and the money it borrowed will automatically add to Spain's sovereign debt pile.
Hollande will find a friendly ear, too, when he pushes for the eurozone to support economic growth.
French officials expect the president to repeat his call, made at a meeting in Rome last week with Italian Prime Minister Enrico Letta, to put "employment growth and stability at the heart of the decisions for the European summit in December".
Hollande is looking for support to boost investment capacity and pro-growth policies across the eurozone, French 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.
Analysts say that level of growth is insufficient to create jobs in Spain, where the unemployment rate is 26 percent, rising to a staggering 54 percent for under-25s.
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 specifically address unemployment. French officials said Madrid was pushing for an efficient use of European resources to combat youth joblessness.
Other issues on the agenda 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.