Both areas were controlled by the Romans for centuries, and both saw migrations by peoples such as the Franks and Saxons once the empire fell. If these groups effectively brought non-Latin languages to both Gaul and Britannia, why did French become more Latin than English?
I think this stems from a misunderstanding of the history of the languages spoken in England.
During the period where England was part of Rome the languages spoken there were not Germanic, they were Celtic (specifically Common Brittonic) and Latin (specifically British Latin). The non-Latin language spoken in, say, Londinium would have sounded closer to Welsh or Gaelic than any variation of English. It was with the Anglo-Saxon invasions and migrations that England acquired a language with Germanic roots, which largely replaced the Latin and Brittonic spoken there. Indeed, there was only a period of perhaps a century or so after Roman rule collapsed and formerly Roman England was on its own before Anglo-Saxon influence began to dominate. Meaning that there wasn't an opportunity for a derivative of British Latin to develop into an "English" romance language.
This has to do with the peoples inhabiting the regions prior to Roman conquest. Speaking primarily from a French perspective, I can tell you that the Gauls were a Celtic people not unlike those inhabiting the British Isles, however, Gaulish is more closely related to Latin than the other languages in its family. Take for example the Gaulish word decameto versus Latin decimus, both meaning tenth. Upon Roman contact with Gaul in 125 BC, they established the southeastern region as the Provincia Romana, which is still referred to as Provence in the present day, and set up Roman institutions and infrastructure in the area such as schools, which Gaulish children would attend, learning in Latin. Eventually with the total subjugation of the Gaulish territory in 51 BC, Latin greatly and gradually influenced the Gaulish language to the point of eliminating it. Gaulish for the most part being an oral language, not much remains of the Gaulish language other than names of places (Paris = Parisii), and mostly agricultural vocabulary in the French language. This resulting language is referred to as gallo-roman, and was spoken throughout the country with few exceptions (Brittany, Navarre).
So there's that. Now you're asking why French became more Latin than English. With the Germanic Invasions, the eventual dominant group, the Franks, didn't have enough numbers to effectively influence the gallo-roman language to the same degree throughout France. The regions of the North, closer to the Frankish strongholds, received a greater infusion of Germanic vocabulary and grammar, and became the regions known as the Pays d'Oïl, whereas the southern regions were minimally affected by the Germanic peoples, with exceptions of the regions that speak Francoprovençal, which was influenced by the Burgundians, and is referred to as the Pays d'Oc. Latin was also extremely culturally relevant with the prevalence of the Catholic Church in France, although it was diverging more and more from the gallo-roman spoken among the population. The integration of the Germanic peoples into the local population also promoted the use of the dominant Latin-based language.
A related question: a few years ago I read "The Secret History of the English Language" by Mick Harper. He argues that it's implausible that England would have completed adopted the language of their Germanic invaders (until the Normans showed up) while other places invaded and occupied by Germanic tribes (France, Spain) kept their Latin language. His alternative theory is that the common language in England before the Romans showed up was proto-Germanic, and English evolved from a mix between that language and Latin (the later Anglo-Saxon kings wrote their chronicles in their own language, but the common people kept speaking "English"). And that France, Spain, Portugal spoke languages related to Latin before the Romans showed up, which evolved into French, Spanish etc. And that the Gallic/Celtic kings and chieftains, while powerful militarily, did not speak the same language as their subjects.
Very iconoclastic theory, I know, but I'm curious: what do professional historians think of this theory? Is there strong evidence that common (not just aristocratic) pre-Roman British, French etc people spoke a Celtic language?