Yes, the mass would be in Latin. It looks as if Richard read at least some Latin, though I don't know how much offhand.
But you don't actually listen to the mass in the same way as a modern one. The priest will often be speaking under his breath (to God, as it were, not to you), and you follow along in your prayer book. We've still got one of Richard's prayerbooks - legend has it he prayed with it the night before the battle - and Margaret Beaufort took it afterwards, crossed out his name, and wrote in her own.
What was in your prayerbook might be Latin, or English, or French, or all three. It might be close to what the priest was muttering that you couldn't hear, or it might be complementary. It wouldn't be like a modern service where you listen to the priest and then make your own scripted response, though it would have portions a bit like that.
I suppose it's a question of how much you think these things change the character of a service.