Gaulish language
The answer to your question in Gaulish language is that the so-called Vulgar Latin, which should be called a Latinized Italo-Celtic idiom instead because the spoken language of the Romans (Osco-Umbrian or Sabellic language and not Latin, already essentially a written language) the 'Proto-Italian' was so similar to the Continental Celtic languages that only the lexicon and the pronunciation differed a bit, and could almost be considered a dialect of Gaulish as it contained the same substratum, unlike the Insular Celtic languages. 

So, in reality no one can assert that Gaulish is an extinct language because we don't know enough about it before the Roman conquest and probably many 'Latin' words were already used by the Gauls before their first contact with the conquerers. At the most 'assimilation' could better describe what happened to that language. Both, the Proto-Italics and the Proto-Celts (Veneti) originally come from the Bell-Beaker culture and lived in a dialect continuum for a long time. In fact, Celtic is more a culture (brought by a Thraco-Cimmerian aristocracy) than a language family except for Brythonic and Gaelic languages which are both quite different from each other because of their respective substratum as mentionned above. Moreover, Proto-English (or Proto-Frisian) spoken by the Belgae was already used in Britain as well as in some parts of northern Gaul (Gallia Belgica) by the time of the Roman invasion, then the Belgic tribes just kept speaking the same language during and after the Roman time.