US President Donald Trump had announced that the leaders would speak about halting the fighting between Israel and the Iran-backed militant group Hezbollah in Lebanon.
According to the French foreign ministry, Barrot's snap visit was a sign of "solidarity with the Lebanese people, who have been dragged into a war they did not choose".
Aoun's six-year term was marred by mass protests, a painful economic downturn and the August 2020 mega-explosion of ammonium nitrate that killed hundreds and laid waste to swathes of Beirut.
The former minister added that residents in several parts of the state are facing power cuts lasting between six and 12 hours, forcing them to stage road blockades at night.