What would two weeks in France do For a person learning French?
If I were to travel, and live in France for two months, while learning French for a entire year already while in college, how much would my language skills improve?
This entirely depends on the effort you make to be around French people and to speak to them. If you mostly stay in a bubble of non-French speakers you will still gain a little just by seeing and hearing the language around you, but it won't compare to the huge gains you can make if you try to thoroughly immerse yourself for at least several hours every day.
Two weeks right now would teach you a bit of official government jargon while you are quarantined and probably asked to fill out forms. You'd likely get quite a bit of clinical jargon as well, with nurses coming in daily to inquire about your health. After the world gets back to normal, two weeks may give you a little more interaction.
I was in France for two weeks once and by the end of that time I could definitely speak and understand French better than when I arrived. I got better at understanding the African-accent French being used by convenience store and supermarket workers who would tell me the price of my purchase.
I haven't stayed in France for two months, but I have stayed in Mexico for two months at a stretch. I definitely improved my Spanish during that period. I travelled solo, so I didn't have anyone who spoke English to talk to, which I think helped. That length of time also gave me a chance to get to know certain people well enough that they would correct my Spanish when I didn't quite get the subtle nuances right, which is very helpful.
I study French and spent two months living in Paris with a French friend after about a year of solid collegiate study and some Duolingo following for a couple years ago so know roughly where you’re at. I expanded my general daily shopping, eating, general exchanges quite a lot. I read and immersed in everything I could grabbing French language guides and tours of museums etc. I didn’t however build much of a deeper use of tenses as conversations weren’t typically very deep given the social circles I ran in as I couldn’t yet express myself that dynamically. That said, I’m soooo happy I had the experience and post trip I have become even more driven to learn the language to drive my level further beyond just getting around to truly realizing full fluency. Your level will improve to the level you immerse yourself.. the language part of the brain is a muscle though and it will get tired to the point that some days you’ll be too brain tired to speak or interact much at all. Every outing is an adventure.. pharmacy, buying face wash, searching for delicious cheeses, ordering from menus, etc. Go out alone away from other English speakers most of the time and find every excuse to think in French that you possibly can. Have fun!
It isn’t how long you stay that matters - it’s what you do while you’re there. I once spent a week living with an elderly French couple in a small village and doing intensive French lessons every day. I learned a lot. On the other hand, I normally spend 6 weeks a year travelling in France in a motorhome, staying on campsites and motorhome aires. It keeps my French from rusting, but I don’t learn a lot because there isn’t enough opportunity for in depth conversation with French speakers. It’s mostly simple conversations about booking in, asking directions and buying things. We chat to people on campsites, but they are often British, Dutch or German and speak English. Sometimes we have a nice long chat with older French people who don’t speak English. It’s not much use talking to young people because they often want to practise their English. So you need good interaction with French people who can’t or won’t speak English.
That would depend on part how much preparation you put in. To get any benefit you would need to be at least a solid beginner before your travel - ie complete the DL tree (to level 5). Trying to do classes in other subjects without some grounding in French would be very difficult - you won't learn the subject and you won't learn French.
I do language classes in Hungary - that is they are teaching us Hungarian and the know we are not fluent. So the teachers use short sentences and simple vocab - and repeat. If I was sitting in a maths class they would not make such concessions.