English came to Britain in the form of Old English around the fifth century AD. The traditional account is that there was a great invasion of Angles and Saxons, but more likely there was a more gradual immigration of those and many other groups besides. Either way, they became the military ruling and landholding elite over most of what is now England. The languages that were spoken there before, something like Welsh Gaelic and some Latin, pretty much disappeared except in Wales and Cornwall; apparently people found it easiest to learn to speak the language of the rulers and gradually lost their native language. There were regional dialects of Old English but the ruling class moved around enough, marrying their daughters to each other etc., that it pretty much held together as a single language. After the ninth century, the house of Wessex ruled the whole country so there was that much more momentum for common use of a single Old English dialect. For a while after the Norman Conquest of 1066, commoners spoke English and the nobles spoke French, but they blended together (especially after the kings lost their French lands around 1200) into Middle English, which in turn evolved into Modern English.
In what is now France, you had the legacy of Roman Gaul. By 500 AD or so, this had been under Roman rule for centuries and practically everyone spoke "vulgar" Latin. Frankish immigrants brought their own Germanic language with them, as did Visigoths in Aquitaine, Burgundians in Burgundy, etc. However, although these "barbarians" also formed a powerful military ruling class, the old Roman provincials were stronger here than in Britain so the rulers found it more convenient to learn their subjects' language than vice versa. Still, their Germanic dialects influenced how it was pronounced; there is a decided tendency to slur those crisp Roman consonants (Latin "rex" becomes French "roi," for instance) and you can hear Germanic "umlaut" vowels in French a lot. Vulgar Latin turned into "Romance" (in other words, "Roman-ish") and gradually into French.
Even then, regional Romance dialects in France were much more different than medieval English dialects. There was a great divide between the "langue d'oc" in the south and the "langue d'oil" in the north, and Provencal was hardly any closer to northern French than Spanish was. When medieval writers spoke of "nations" (thinking largely of language), they saw the "French" as a quite separate group from the Aquitanians, Burgundians, Poitevins, Normans, etc. It was really the spread of print media and of more intensely centralized government administration in the modern era that gradually drove acceptance of northern, Parisian French as somehow "standard."