Have you considered the possibility that this child might have a generalized social phobia? Does he express concerns about fears of being embarassed by making mistakes in class, especially since he is in a new program of French immersion?
Does he express any fears of his teachers or other authority figures?
I suffered from this problem from a very early age and was not finally correctly diagnosed until 5 years ago ( I am now 53). I found the book "Dying of Embarassment" helpful. Perhaps some of the strategies there would be useful.
Is there a group for children with anxiety available?