Perhaps ATL Muslim armies were able to take Tours and eventually Paris in the mid 8th century. I'm not sure if the Umayyads would have instituted a dhimmi system and let Christianity survive with severe penalties, or convert the Frankish people directly to Islam. If the Franks were made dhimmi, I could see a mixture of Christian Latin and Islamic Arabic (as in Spain), with the Gallican church surviving to some degree liturgically and contributing to the mixed culture. I think this possibility would be diminished if the Franks were forcibly converted to Islam with little chance for the survival of vulgar and liturgical Latin. I think this question also revolves around the sophistication of Frankish Christianity and the development of intellectual culture in this region. I know absolutely nothing about 8th century western European rural life, so I can't comment on that tangent.
Culturally, who knows? Perhaps Muslim Spain of the same period provides a similar example of the mix of languages, religions, and cultural sensibilites. From my (limited) understanding, Muslim Iberia was a somewhat culturally fluid place, with Jews, Christians, and Muslims interacting intellectually and culturally to varying degrees over time and with varying degrees of personal freedom for the dhimmi. Maybe that's what would have happened in France, but no one knows for certain.