The law bans all wearing of obvious religious signs such as Muslim headscarves, Jewish skullcaps and large Christian crosses by any pupil at school in France.
The French Government says it wants to make all children equal.
It says that as schools in France are not religious such things should not be worn.
Many Muslims and Muslim leaders around the world don't want the ban enforced - they say it is the right of any Muslim girl to wear the headscarf.
The kidnappers in Iraq are believed to be the same group of extremists who captured and killed an Italian journalist there last week.
A film they sent a television channel said the kidnappers wanted France to reverse the ban within 48 hours.