France was historically very interested in the Near and Middle East, though colonially somewhat less successful than the UK; Napoleon sailed to Egypt in 1799, and later the French Republic protected Lebanese and Syrian Christians, up to some point in history. People from the Levant still like to study in France (incl. Nassim Nicholas Taleb). Hence, France is considered a strong and culturally developed country in the region.
And unlike the UK and US, they had no historic bad blood with Iran (Mossadegh et al.)
A more recent influence came from the Sykes-Picot Agreement [1].
[1] https://en.wikipedia.org/wiki/Sykes%E2%80%93Picot_Agreement
And French is still language of educated class in some places in Levant, esp. Liban.