"half of all births in France are already to Muslim parents."
Where did you get this? The population of France is about 60 million, with an estimated 5 million of Muslim background. With a national birthrate of about .12, and assuming that half of Muslim population is female (which is high), for half of all births to be to Muslim parents, half of all Muslim women would give birth every year. Does not compute.
At any rate, the French census does not record ethnicity or religion.
To understand present day demographics in Europe (and France in particular) you must look at both age distribution, and the age when births occur. Simply looking at population percentages alone will not get you anywhere close.
The Muslim population of France is much, much younger than the ethnic French, and the age at which Muslim women have children is much younger. Hence there are many more Muslim women giving birth than their percent of the population would indicate.
The result is not just that a disproportionate number of all young people in France are Muslim, but that 50% of all births in France are to Muslim parents. Although this is a relatively new phenomenon, one early result is that 25% of the enlisted troops in the French armed forces are now Muslim.
Source? The French government has refused to allow collection of census data based on religion. Hence there are no "official" sources (can you say, "DENIAL"?).
The Catholic Church has stepped into the gap, and their numbers are considered the most reliable in France. Based on the Catholic Church's estimates (including the Catholic estimate of the current Muslim population), a birth rate of 1.3/woman among the ethnic French is all that is needed for 50% of all births in France to be Muslim. This is well within the present day norm for "old" Europe.