Not at all. Paris is named for the Parisii. For one that is the Latin version of the name — although the Parisii had coinage it has no script on it to confirm the native spelling. If the Roman spelling is accurate it has been suggested it is cognate with Welsh Prydain (Britain) from Celtic *Pritani, perhaps from a Proto-Celtic *Kʷritanī, *Kʷritenī, whence Welsh Prydyn (“Picts”), Old Irish Cruthne, Cru(i)then-túath (“Picts”), from Proto-Indo-European *kʷer- (“to do”) but exactly how and what it meant is uncertain (in both Gallic and Brythonic kʷ becomes p — "Britain", and via Welsh "Brythonic", is via Latin, from the Greek Prettanía, again from Celtic *Pritani, which just illustrates why you can't necessarily trust the names used by Roman historians).