In an interview with the newspaper Le Monde, Le Pen suggested the ban is a measure increasing "freedom of expression" by undercutting "politico-religious fundamentalists," Radio France Internationale reported.
"Freedom of expression is non-negotiable," she said.
Many Muslims believe women should dress modestly in public, with a scarf covering the hair. Under former President Nicolas Sarkozy, France banned garments like the burqa that cover women's faces.
Orthodox Jews believe men must wear a head-covering, often the close-fitting skullcap known as a kippah or yarmulke.
In an interview with TF1 Saturday, Le Pen said the "kippah is not a problem in our country" but she said it should be banned to show fairness.
President Francois Hollande and Education Minister Vincent Peillon denounced Le Pen to reporters Friday while they attended a memorial ceremony at Drancy, the site of a transit camp for Jews being sent to concentration camps during World War II.
"Everything that tears people apart, opposes and divides them is inappropriate," Hollande said.
Jean-Francois Cope, who is seeking the leadership of Sarkozy's UMP, accused Le Pen of "mixing up secularism and the eradication of religions."
Le Pen, daughter of Front National founder Jean Le Pen, came in third in the presidential election. She refused to endorse Sarkozy in the runoff.