Is it permissible for a Muslim woman residing in France to remove her headscarf at work or during study, if that is a condition for obtaining a job or an educational opportunity, provided she wears it immediately upon leaving these places?

If what is meant by khimar is that which covers the head and chest, then it is an obligation by consensus of the jurists. However, if what is meant by it is the face covering, then the matter is less strict, and its covering is likely obligatory, but there is no harm in taking the concession in matters of ijtihad (independent reasoning) to remove hardship. If the excuse that permits removing the khimar ceases, then she must wear it.