I think the Lutetia question is misleading. The Romans did not found Lutetia: it already existed and it had Gallic or Celtic origins. The only thing that happened in 52AC is that the city was occupied by the Romans.
Also, the "franks" question should also accept "merovingians" and "salians".
Frequently when Romans would conquer an area they would found cities in areas where locals had already established small farms, settlements, or villages. Sometimes they would use local names for the Roman city.
Several pages in the wikipedia refer to the year 508 AD when Paris became the main recidence of Clovis. Just said, but I did not further research on that date.
Also, the "franks" question should also accept "merovingians" and "salians".