Historical linguist Brigitte Bauer has brought up substantial evidence* that Gaulish and Latin were highly similar languages.
Nicholas Ostler has argued** in the same sense, saying that Latin could only have replaced Gaulish so quickly if the grammatical structure was (nearly) identical and the two languages shared enough similarity in vocabulary to allow for a word-to-word replacement, as was the case with the replacement of Aramaic by Arabic. Iberian and Dacian Celtic were probably also close to Latin, perhaps all derived from a Hallstatt Celtic mother tongue.
* you can read about this in
Archaic Syntax in Indo-European: The Spread of Transitivity in Latin and French and
The Emergence and Development of SVO Patterning in Latin and French: Diachronic and Psycholinguistic Perspectives
** in this great book on diachronic sociolinguistics
Empires of the Word: A Language History of the World
At last this evidence is coming out , that Gaulish tongues and Latin where very close :
just an exemple with Rex in Latin and Rix in Gaulish .
Furthermore if you listen to the sound of the Latin language , it sounds dark like a language from the north .
So my conviction is that actual french is in fact gaulish that has been latinized , as the latin had the advantage to be written .
From all the so called romance languages the French is the one that sounds the most like Latin , because it latinized Gaulish ,
and Latin was a close cousin to Gaulish .
Then it destroys the awkward theory that Gaulish languages disappeared , and the Gauls got rid of their langages to adopt the Latin .
No group of people abandon their language unless they are overwhelm by superior numbers .
And I would add another hypothesis ; it is well known that English is the closest germanic language to the Romance languages .
The mainstream explanation is it's because of the latin and the french conquests .
It could be also because the celtic tribes in England where speaking the same Gaulish languages ,
as an example the word "car' probably derive from the gaulish " Char" .
( In England at this time you could find tribes with the same names found in France : the Parisii , the Catalauns , etc )