You neglect the fact that the 'indigenous' population of France before the Great Migrations (of mainly Germanic tribes) was Gallo-Roman, and by the end of the Roman era (5th century AD), the populace spoke a dialect of Vulgar Latin, which evolved into a distinct "Gallic" Latin over the following centuries. Note however that the ancient Celtic (Gaulish) language spoken in France before the Roman conquest has had minimal impact on the French language, largely thanks to centuries of strong Romanisation. Germanic influence was undoubtedly greater, estimated at some 10% of the modern French vocabulary. There was also some influence on grammar and pronunciation, although the extent of this is debatable.
The Frankish invasions, which started in earnest in the late 5th century AD, added a Germanic admixture to both the population and pre-existing language ("Gallic Latin", if you will). However, the existing population and language was by then firmly defined, and the relatively small number of Frankish invaders (despite their conquering) only influenced the French language in a minor way, eventually adopting the predominant native language, with minor influences by their own Germanic mother tongue (mainly Frankish). This situation was mirrored to some degree in the later Norman invasion of England (where the roles of Germanic and Romance languages are in fact reversed).
If I were to make an educated guess, the predominant factors behind the native Gallo-Roman (Romance) language winning out was the overwhelming greater population that spoke that language rather than Frankish/Old Germanic during the formative years of France/the Frankish realms. Also worth noting is that at the time of the invasions, the native Gallic population would undoubtedly have been better educated and hugely more literature, thanks to the Roman influence. The Germanic peoples at the time however, were only just shedding their illiteracy, making it rather hard for their own language should supplant the existing one.
Note:
@AlainPannetier provided a great source (book) in the comment section that states that the estimated invading population of Germanic Franks was around 5% of the native Gallo-Roman population at the time of Clovis (first king of the Franks.) Indeed, the fact that post-Roman Gaul has a well-established Gallo-Roman upper class also meant that it would have been much harder for Vulgar Latin to have be supplanted at the time.
