Good question! Sorry for my delay in getting to it.
The Jews in England generally migrated to Northern France. They'd migrated to England from there, and the close distance would've made it the obvious choice. Unfortunately for them, as you note, France would expel Jews soon afterwards, so they were dislocated again.
Jews from Northern France generally moved West to German-speaking areas. In the long term this meant that English and French Jews were simply integrated into the Ashkenazic Jewry in general. Jews from southern France (the expulsion of 1306 included much of southern France) generally went to Spain. While some Jews did return to France in 1315 before being expelled again in 1394, the community was far smaller than before.
As to why this didn't make waves in Jewry the way Jews expelled from Spain and Portugal did--the Jewish community in England was far smaller and less influential than in Spain. When Jews were expelled from Spain they brought with them a particular Jewish culture that was seen as prestigious, and formed a significant portion of the Jewish community in their new homes. Sometimes these two factors combined to make Sepharic Jews the dominant community in the regions they arrived at, the preexisting community either becoming a minority of local Jews or assimilating in to Sephardic Jewry.
And for French Jewry--the French community was larger and better established than the English community, so you might've expected them to stick around. But the German and French Jewish communities were already pretty closely tied, so they simply integrated into Ashkenazi Jewry too. One could imagine that French Jewry had produced enough of its own cultural material to survive as a Jewish subculture even when expelled, but it didn't. I'm not sure there's a documentable reason for this, but presumably they did not see themselves as different enough from other Ashkenazi Jews to maintain a distinct communal identity. Or they did not maintain enough of a concentration in one place for a self-sustaining community, but we don't have the kind of detailed demographic data to prove that (that I know of).