You understand the distinction between Islamic veils/headscarves (which clearly imply religious affiliation) and clearly non-religious, headscarves worn by many style-conscious, but secular, women?

Your misunderstanding may come from terminology - a headscarf need not be religious at all, and headscarves which are not religious (it is easy to tell the difference) are NOT banned.

The headscarf to muslims is not really a religious symbol like say a priests clothes or a nuns habit. It is a piece of clothing that is required (considered mandatory by most schools) to be worn by a woman to preserve her modesty. In that viewpoint, it is like pretty much every other piece of clothing . Are pants or tops religious symbols?

Does it clearly imply religious affiliation, or cultural affiliation? Either way, it's such a petty and arbitrary distinction and I'd guess that a Muslim girl in a French school wearing a regular head scarf would still get hassled and forced to remove it.