The use of Gaulish after the Roman conquest is a most controversial issue. The truth will never be known. Careful examination of the evidence may give some indications. The Gaulish we know is what the Germans call a "Trummersprache" a language in ruins. Only debris of this ancient language have survived by accident. Although there is far more Gaulish left to study than there is British, Goidelic or Celtic Pictish the rich medieval sources that exist for old Irish, Middle Welsh and Breton have no counterpart in Gaulish. Before the conquest Gaulish nobles sent their children to Rome to be educated. Notables from the region of Marseilles sent their children to the schools there to learn Greek letters. There was therefore a well established bilingual tradition among the privileged especially in Latin and Gaulish. We may therefore expect that the privileged classes adopted Latin very quickly after the conquest and the suppression of the revolts in the first century.
The survival of Gaulish should therefore be expected, if at all, among the lower orders only. The peasant is silent but the artisan class left their marks on the portable objects that they manufactured. Gaulish words appear with potter's stamps, inscribed on rings, plates, coins etc and, especially interesting, on loom weights where we find gems such as "GENETA IMI DAGA VIMPI" (I am a good and fair young girl. Here GENETA is as Welsh geneth (young girl), IMI (I am) and DAGA (good) Welsh da, Old Irish dag and VIMPI (fair, pretty) Welsh gwymp. There are also longer inscriptions recording accounts, dedications, magic spells etc. but none are later than the second century.
Gallo - Greek inscriptions date from the third century B.C.E to the first century C.E. Caesar tells us that the Gauls used the Greek alphabet when they needed to write something down. He mentions the archives in the Greek alphabet he saw among the Helveti.
Gallo - Latin inscriptions appear immediately after the conquest on stone but seem to peter out about a century later. The Coligny calendar (on bronze sheet) seems to date from the end of the second century C.E.
There are 16 inscriptions on stone in Gaulish using the Latin alphabet.
This should be compared with 10,000 Latin inscriptions on stone.
French has a (disputed) list of some 160 words whose origin is certainly or very probably Gaulish.Many more are suspected among the dialects. There are references to Gaulish being spoken down to the fifth century. Later references, such as Gregory of Tours who gives equivalents for Gaulish words are probably not good evidence for the language being spoken because all the words cited are nouns. Very many place-names are of Gaulish origin and many betray the presence of landowners with Gaulish names. Most of these will have been coined after the conquest.