Hardest yet to come for France's Hollande

French President Francois Hollande addresses journalists after a meeting at the Elysee Palace in Paris, September 9, 2014. REUTERS/Christian Hartmann

PARIS (Reuters) - A bitter public attack by a jilted ex-partner, a cabinet melt-down and the admission of broken economic promises have meant an uncomfortable three weeks for Francois Hollande.

But the hardest is yet to come for the French president, who this week embarks on a struggle to convince Socialist allies, the French people and his European Union partners that he is still fit to run the euro zone's second largest economy.