US relations with France were jolted last year when Hollande lined up with Obama to strike Syria, punishing it for its use of chemical weapons, only to be left on hold at the very last minute when the White House acceded to a Russian idea for a negotiated outcome.
There is also hostility over the US National Security Agency's surveillance campaign and swelling accusations, fed by Hollande himself, that US cyber-giants such as Google and Amazon are dodging French taxes. Yet France is seen by the US as playing a linchpin role in combating jihadism in Africa, where French troops have intervened in Mali and the Central African Republic.
"Hollande's state visit to the United States, only the fourth state visit from any foreign leader since Obama took office, holds much in the way of symbolism. It is an important signal that France still matters, and that the time is right to turn to historical partners for advice, support and vision," noted Guillaume Xavier-Bender of the German Marshall Fund, a transatlantic think-tank, in Brussels.
The two presidents "have a quality relationship", says an official at the Elysee presidential palace. "The two regularly contact each other and frequently talk about various crises."
Among the French public, the picture is somewhat different. Obama still has a fund of popularity in France, but a few photo-ops with him are unlikely to dispel the start of what may be Hollande's annus horribilis. Last week, his popularity dipped to a new low with just 20 per cent approval rating, the lowest for any modern French president.
The cause is only partly his affair with actress Julie Gayet and his ditching of first lady Valerie Trierweiler. The episode has transfixed media abroad, which caricature the 59-year-old French President as a rake heading out on a scooter to a grubby tryst. In France, the affair is viewed far less as a moral issue or as a source of sniggering, but as something messy and unpresidential. A far bigger deal, for many French, is Hollande's fumbling management of the economy, where he has gained a reputation of a ditherer, vulnerable to flipflops when pressed by lobby groups.
After vowing - and failing - to reverse the rising trend in unemployment by the end of 2013, the Socialist has now recast himself as a Social Democrat eager to foster a more business-friendly environment. Polls say the makeover has failed to give him a bounce with the public, and the biggest doubters are in his own party.
On Wednesday, Hollande - a graduate of France's elite bureaucrat-making school and until his declared conversion, a tax-and-spend loyalist of his party - will arrive in San Francisco, where he and his entourage will get a first-hand view of the freewheeling cyber-economy.
He is due to meet the chief executives of Google, Facebook, Twitter and Mozilla - and may also meet Carlos Diaz, a French entrepreneur who in 2012 campaigned against his high taxation on corporations.
