I am sure there are many studies on that question. I have none with me today, but I know so many researchers who have studied the issue that I am convinced the answer is out there.
All of the studies show that proximity is the main factor in the parents' choice of a school. It is first and foremost a proximity issue.
We have to encourage all exogamous couples to understand that if the immersion school is a little closer, and if the French language school is further away...