Hi Pillowcase,
Redoublement is not so much as popular as obligatory at certain ages - CP the parents have no choice, ditto 5° if the child is not at the moyen - usually French and maths are the clinchers - (especially if the school is private) ditto 3° if no brevet and the same applies to the BAC years.
Private schools will redouble children to keep up standards and class attainment/averages levels. My son ended up redoubling CP (huge long traumatic threads, now deleted). I was very against it but he is now a happy and confident student, doing extremely well and it was, in light of all that has happened since, a Godsend. Other parents in his class (private)withdrew their kids and sent them to state schools rather than redouble. One of my son's friends, who had lower marks than he did in maths and reading, is now struggling in (state) year above, with 5 hours of state provided help per week. It will be interesting to see how they are both doing, my son and hers, in a couple of years.
BTW, redoubling in CP used to be a huge blackmark against a child (hence possibly why parents are still moving children to avoid it, and why it is as you have found in your area 'unpopular') but I think that times ahve changed and I would rather he stayed down a year young and then spent the rest of his (rigorous, French!) school career bopping along than struggled and struggled later on (as one of his siblings has done).
Speech over.
Come to Toulouse NN. I love Toulouse!