Short answer: Yes.
Long answer: Master's programs in europe is great if you are looking for MSc or MA. They offer relatively few professional degree program in europe, and those that do are relatively new and not really established among the field yet. To focus on your point on how to apply for european institutions, it's just like applying to schools in the US, only no GRE and you don't have a centralized application system like Common App, SOPHAS, or whatever they use.
A good example here is https://mph.ehesp.fr/apply/admission-requirements/, an mph program from the new School of Higher Education in Public Health that was just established in France.
Just make sure you have a decent level of native language that they speak over there though. The program itself might be in english, but your daily lives won't be.
Good luck with your application