Latin didn't die. It just became all the other Romance languages. That's one of the ways languages "die". They simply develop into something else. As a historical linguist, a large part of what I do is trace these changes. When we speak of Latin as dead, we're referring to a period of time in the past where the language that became Italian was distinctly different enough to call it something else. But that distinction is somewhat arbitrary, and you could just as easily call Latin "Italian".

In the case of Gaulish, what you have is an example of one language (Gaulish) being replaced by another (Latin). Gaulish stopped being the man language, but parts of it survived in the local Latin dialects as what we call a substratum. When a language replaces another in a single geographic area, the old language influences the new, ant its these influences which helped the local Latin dialect become French.

The other big way languages die is that the people that speak them die. What I'm going to call "flash-genocide" (i.e. outsiders wiping out ppl in a very short timeframe) committed against all speakers of a given variety would kill the language without leaving much influence on the language replacing it, though this isn't really something that's happened often in recorded history.