Saudi Arabia is Iran's main regional rival and is a key backer of Syria's rebels.
While in Beirut, Hollande said France will give "full assistance" in the investigation of al-Hassan's assassination, saying "the Lebanese and the world want this. There will be no escape from justice."
Al-Hassan was killed a day after he returned home from Paris, where his family has been living for years.
"Even though Lebanon is very close, it should not be the victim of this crisis," Hollande said referring to Syria's civil war. "We renew France's full support to the stability, unity, independence and safety of the territory of Lebanon."
France, the onetime colonial ruler of both Syria and Lebanon, has been one of the most outspoken Western critics of the Assad regime. France announced in September that it had begun sending direct aid and money to five rebel-held Syrian cities as part of its intensified efforts to weaken Assad. It was the first such move by a Western power amid mounting calls for the international community to do more to prevent bloodshed.
French officials have acknowledged providing communications and other non-lethal equipment to Syrian rebel forces, but say they won't provide weapons without international agreement. Paris played a leading role in the international campaign against Libyan dictator Moammar Gadhafi last year.
France still wields wide influence in Lebanon and has about 900 peacekeepers deployed near the border with Israel.