I am a student of another EU country and in 2014 I did a 3 month internship in France, in a French company. I was 22 at the time and the total bonus for the internship was about 3200€, spent less than 183 days in France. The thing is, I was on academic leave while doing the internship - does that qualify this as professional activity? Of course the internship was done in the subject of my studies and we had a proper convention de stage with the school and the company, just like any other intern.
I don't think being a foreign student makes any difference. Income sourced in France must be declared according to the same rules. Beyond that, you might or might not benefit from a tax treaty and would not incur any income taxes on €3200 anyway (you should already have paid the mandatory tax-like insurance contributions as applicable) but you might have to submit a tax return, even if you are not a resident.
In other countries, taxes would probably have been withheld from your pay through some “pay-as-you-earn” scheme, even for an internship. France still uses traditional tax returns but that does not exempt you from the requirement to declare your income. If you do have to submit a tax return, you have until June to do it (and not all the info/forms for 2014 are online yet, you are expected to do it in April-May 2015).
Furthermore, there are a few special rule for “young people” (French citizens or residents and foreign residents alike). In particular, if your internship was mandatory (in the sense that your school required it to qualify for a degree) and lasted at least 3 months, declaring income under about €17000 per year is not required.
In practice, if you are registered at a foreign school or university, I suspect it's more difficult for the tax office to know whether your internship was mandatory or not and you could probably get away with not doing anything even if you internship does not technically qualify. I suspect they would not bother initiating an inquiry for €3200 in any case (after all, they could at most impose a fine for failing to fulfill some obligation or something like that but there would still be no taxes to recover as your income is under the threshold of the first tax bracket). But I don't really know.