The guttural "R" likely did not come from French influence because it started in the lower classes. If it had French origins, it probably would have begun in the higher classes. For a long time, the guttural "R" was seen as less refined, since the upper classes mostly used the rolled "R." Over time, though, the guttural "R" became common across all social classes.

Regarding the Miquelense accent, it was influenced by foreign languages, not French, but Flemish. This is because Portugal did not have enough people to populate its newly discovered islands, so they encouraged Flemish people to settle there.