Well, as it happens, a number of ‘Hebrew’ names are not actually Hebrew in origin at all. Moshe, for example, is ancient Egyptian–it’s the same root that appears in the Pharoanic name Thutmose. Miriam is also in all likelihood Egyptian in origin. (The origin of Aharon is not clear.) Mordechai is Persian and is derived from the name of the pagan god Marduk. Esther is also Persian and is derived from the root for ‘star.’ Some of our names are Aramaic as well.
The custom of double names, a shem kodesh and a shem kinnui, goes back at least as far as Hellenistic times. Famous examples include Philo of Alexandria, whose shem kodesh was Yedidiah, and the historian of the Roman-Jewish wars, (Titus) Flavius Josephus (Yosef ben Matisyahu) who was in modern terms very frum. You can see the same custom in the Christian scriptures with characters named Shimon Peter and Shaul Paul. The custom of dual names continued on through the Middle Ages (in Muslim lands some Jews even used the name Mohammed which is, of course, unthinkable today) to the present. The fact of the matter is that our names reflect our long and varied history, almost all of it spent as a small (and often oppressed) minority surrounded by less than welcoming majorities with whom we of necessity had to interact. Today in EY and in some enclaves in North America and Europe, we do not all have to interact on a daily basis with non-Jews, and in those enclaves people have reverted to one “Jewish” (not necessarily Hebrew) name.
Rashi was indeed a Francophone and borrowed French words into his writings. One notable French borrowing from that period is to bentch. This ultimately comes from the same Latin root as benediction and was borrowed from Latin through French.
If people today, like Oomis, want to give their children only Hebrew names (thus. I presume, avoiding names like Moshe and Mordechai), that’s their choice and their right. My personal opinion is that ‘mixed’ names like Menahem Mendel, Dov Ber, Tzvi Hirsh, and the like and borrowed names like Shprintza (from the Spanish Esperanza), Gittel, Fraydl, and so forth are the names of our ancestors and reflect our long and difficult history, and I see no reason not to use them if parents so desire. Just so, the custom of giving a “Jewish” name (of whatever etymological origin) and a vernacular name (today probably an English one) has been part of our history for more than 2000 years, hardly an innovation. Our ancestors found this practice useful–in some small way it may have facilitated our survival in difficult times–and many still find it useful.