> Based mostly on Northern Italy's languages (mainly Venetian and Genoese) and secondarily on Occitano-Romance languages (Catalan and Occitan) in the western Mediterranean area at first, Lingua Franca later came to have more Spanish and Portuguese elements, especially on the Barbary Coast (now referred to as the Maghreb). Lingua Franca also borrowed from Berber, Turkish, French, Greek and Arabic.
Technically no. Especially not the northern dialects which modern French is based on. Arabs/North Africans/etc. just called all Western European Franks. The actual dialect/pigeon language used in the Mediterranean and called "Lingua Franca" was mainly based on Northern Italian, Occitan and Catalan (so barely related to modern French).
Which was a language that was barely related to modern French (besides belonging to the same Romance language sub-branch which includes Catalan, Occitan and most Northern Italian dialects, coincidentally places where most of those merchants who introduced that language came from).
So, very closely related to French?
~320M French speakers globally (220M native, official language for 29 countries)
~559M Spanish speakers (~480M native, 20 countries)
~1.1B Mandarin speakers globally (a few countries, mother tongue in ~20 countries)
~1.5B English speakers globally (~400M native, official language for 67 countries)
So for much of the world it seems pretty clearly English (& has been since WWII) and French is in the “second” tier competing with Spanish and Mandarin (probably just behind Spanish & Mandarin in terms of penetration lingua franca is about being the bridge language).