The shooting occurred close to the cathedral city of Chartres, south west of Paris, at 7.45am on Tuesday morning as Hana Gharbi, a French teacher, drove her daughter and a colleague to the Saint-Paul-de-Brou school where she worked.
Just outside the village of Mignières where she lives with her daughter, the road was blocked by a white van. A man wearing a mask and carrying a hunting rifle approached her car, broke the window and shot Gharbi twice.
Gharbi was taken to a nearby hospital and later transferred by helicopter to the Pitié-Salpêtrière hospital in Paris. She was in a stable condition on Tuesday evening.
Police are hunting for Gharbi's ex-husband, known as Michel B. The couple separated around two years ago.
The white van used to block the road was returned to a car rental agency later on Tuesday morning. Police believe Michel B may have returned home before fleeing.
Newspaper Aujourd'Hui reported that the couple had a strained relationship, particularly with regards to their 12-year-old daughter.
"The rare times that he was here, things didn't go well," said one neighbour of Hana Gharbi, according to the newspaper. "On several occasions she got scared and called the police. But I saw her this weekend for her daughter's birthday and she didn't seem more bothered than usual."
A friend of Michel B's told the newspaper the couple's separation had been "very conflictual." The friend added that Michel B had been "very unhappy about not seeing his daughter and seemed ready to do anything to get her back."