What happens if a language other than English is used over the radio?
During the 1990s I flew into countries on every continent except Antarctica. As an American English speaker flying U.S. registered airplanes, I never had a complaint that a controller had trouble understanding me, and I was always addressed in English by the controllers. Sometimes, though, I would have trouble understanding the controller's accent and would have to ask them to repeat their instructions.

As you mentioned, in some countries the controllers will address the pilots of that country in their native language. Personally, I always felt that compromised the smooth functioning of the system to a degree, because it denied a good bit of the overall picture of what was happening to the pilots who didn't speak that language. For example, if two airplanes preceding you are being rerouted for some reason, but you can't understand what they've been given (and which you're probably going to be given), you're not as prepared for the reroute when it comes through to you in English.

Even if controllers spoke to you in English, they would typically pronounce place names and fixes as they are pronounced in the native language. My first flights in France were a real problem in this respect. The French controllers were speaking good and understandable English, but the French pronunciation of the place names did not match our English rendition of the names we were seeing (and had never seen or heard before) on the IFR maps (no glass cockpits back then for us). In a couple of instances, we had to request that they spell the names, which didn't make us popular. On one occasion, when we made such a request, another pilot came on frequency and said, "He means ...." and gave us an English transliteration if you will of what the controller was saying.

Interestingly, the worst time I ever had understanding a clearance was one from a nominally English speaking controller. We were talking to Scottish control, and received a reroute into Amsterdam from a controller with a very pronounced accent (Glaswegian?). All I was able to get was that at the end he was turning us over to Dutch control and the frequency. I went over to the Dutch, and asked for them to restate what our new clearance was, and I apologized, explaining that I had been unable to understand Scottish control. His first words were, "That's okay, we can't understand them either."