When I googled 'redouble the year' I was directed to French sites, and I noticed that it is indeed used. Now, I want to have a confirmation from English native speakers. Can 'redouble' be used for 'repeat'? I'd be very grateful for your help.
No, it can’t. The only use of redouble I can think of immediately is in redouble your efforts, with the sense of ‘work much harder’. If you have to repeat a course, you can say just that or, more simply, do the course again.
Although the dictionary definition of redouble is to double or to repeat, it is seldom used by native English speakers to mean this.
I strongly suspect that most English speakers would understand it to mean "to double something that has already been doubled. It is used in this exact sense in the game of Bridge.
The reasonably common idiom "He redoubled his efforts", can then be read as "Having already doubled his efforts, he doubled them again".
Again, this is not the dictionary definition, but it's my strong sense that that is how most people would understand it.
"Repeat the year" is what English speakers would say. There is no reason to look for an alternative phrase.