I did Erasmus last (school) year and it was brilliant, am jealous of any DC that's still got that ahead of them....
The tuition money goes to the department sorting out your uni stuff for free, examining you, supporting you while you're away e.g. it was made clear to use we could come back and use the libraries/MH services, or talk to anyone in the department for advice whenever we wanted to. Our department and Erasmus coordination are awesome though, might not be the same everywhere.
If improving your language is the aim then I'd say uni is an excellent option. All the essays you have to write and all the set texts they make you read... My uni wouldn't let me write in English (host unis allowed that) and all my grades counted towards my degree (not always the case) so I really had to put the work in, I did so much reading, and my grades/grammar are loads better now, plus reading quickly is much easier. Bear in mind that they might let you use a certain number of ECTS on a language course (B1+), which I did in a four-week holiday, so I had one less class to worry about during term. Oh and in both my unis they did let you write 'Erasmus' on your papers so you're not marked down too horrendously on grammar. Have never worked as hard as on my Erasmus year, never drunk so much red bull and amazing wine, never enjoyed it as much or discovered so many new interests in and outside of school.
Paris uni was tougher than Austrian uni in terms of pushing you re: analytical thinking & originality (and 20 min presentations, though one prof let me do two extra extended essays instead, bit of a raw deal), Austrian uni was tougher in terms of the sheer volume of stuff you need to know for the exams. Though the department head did say that four VO (Vorlesungen) was too much, but I needed the ECTS and just exams, no coursework, seemed too good to pass up...
I was lucky with rent and accommodation both times so won't talk about that.
Also I would say head for a city, not a tiny town somewhere with British Council, just my humble opinion (aware that some people will have had great times in small places). As a student a city is just made for you, so much to do, so many people in the same situation.
If anyone's DC are going to Paris & they like to babysit they should look up Speaking Agency. French families pay you to speak English to their kids and I got stg like 152 euro a week for 13 hours. I did it so it could go on my CV and I could spend time with adorable toddlers :) and the money paid for my M&S food habit
Erasmus grant was incredible, it wasn't advertised so was a lovely surprise
I got I think around £2300! Because of the language course I took in holiday time they gave me an extra £400 when I came back in Sept.
OP if you like, PM me for the name of the French uni I went to, which I'd definitely recommend 100%
what a ramble. sorry! I like talking about Erasmus :)