I am currently taking french 2 and would like to take korean, japanese, or chinese next semester. Does anyone have any experiences with doing this? I took french in high school and a lot of the things we are learning in french 2 and are supposed to learn in french 3 are review for me so I think I might be able to handle the workload of two language courses. Also out of the three which would you recommend out of the three (I would like to do study abroad in at least one of these countries).
I’ve taken multiple languages concurrently for probably the past five years, and haven’t had a problem yet. I think you’ll be fine being the French isn’t in the same family as any of the languages you are considering, which avoids the usual problem of potential confusion between the two. Be prepared for people to ask you why on earth you’re taking multiple languages. Apparently it’s baffling to others to want to be multilingual 
ETA - in trying to decide which of the three languages to pick, consider the size of the department and depth of typical course offerings. One language may only be available up to the II level, while another may offer many upper level classes.