Having charged up in their massive home market, Chinese electric-vehicle-battery firms are becoming major export players, too. The West’s efforts to protect its own markets might prove too little, too late.

Chinese firms are also eyeing big new factory expansions in Europe itself, and in U.S. free trade partners, as a way to sidestep current and future import restrictions—much like Japanese carmakers did in the U.S. in the 1980s.