can I learn French in Germany/ Sweden for free over the period of 4 weeks?

No. First of all, education is not "free" for foreign students. Short-term language programs are conducted by private fee-charging schools. And language schools in Swedish teach Swedish (or some English-language schools for Swedes), while those in Germany teach German (or some English-language schools for Germans.

NO freebies! You get what you pay for.

a) There's no such thing as 'free education'; there might be low or no tuition fees, but that's not quite the same thing - you still have to pay your living costs etc. for the four weeks, and possibly some study materials also. In any case, that doesn't apply to you, only to EU citizens.

b) Why would you go and study French in Germany or Sweden, surely French is best studied in a French-speaking country? (Duh!)

No

maybe

No; you won't be eligible for free programmes.

There are no easy ways to learn a new language but there are cheap ways. You do not need to go to a class. Buy a dictionary and grammar book and start learning. If you can do it in the country itself, so much the better. Of course if you can find a job it will be cheaper still.

I learned Italian whilst looking after children. My housing was free, I did a chapter of grammar and some vocabulary every day and practiced on the children who were very polite about it all. By the end of the summer I was fluent. Learning a new language is really hard work. Four weeks is nowhere near enough time.