How widely were German, French and English each used as languages of science in the Europe of the 19th and early 20th centuries?

Greek linguists at the time mostly did German, and some did French. Of the main antagonists, Psichari only wrote in French—but then again, he lived in France. Hatzidakis mostly wrote in German, though he could write in French if he had to.

When I was studying in Greece, I heard distant echoes of a “German school” and “French school” of linguists: you picked your main language and aligned yourself to it. English was used, but not by Greeks; as a language of Greek linguistics it was marginal before WWII—about the same ranking as Italian. (They were distant echoes, because that era had ended by the ’60s. The linguist I heard the echoes from, Δικαίος Βαγιακάκος – Βικιπαίδεια, was born in 1917.)

I have seen instances of Dutch linguists working on Greek (Hesseling) translating their stuff into French to get it read. Sandfeld’s Linguistique Balkanique was ignored until he translated it from Danish to French. So yes, getting your stuff translated was a must if it wasn’t originally in French or German (or, OK, English and Italian). The only language I noted in my reading other than those was Russian, and there wasn’t much of that. (A bit more in Byzantine studies.)