Can French shops refuse to take change?

No, the law (R.642-3 of the Code penal) says it is an offence to refuse to accept payment in coins which are legal tender. However, an EU law (regulation CE no. 974-98 of the Council of May 1998) which was put into French law (Code monétaire et financier article R112-2) states that a shop may refuse this if there are more than 50 coins.

The shop may also require another form of payment if they ask you to pay the exact price and you cannot.

As a matter of interest, shops are also not allowed to refuse payment in notes, no matter how high the value (eg. if someone pays for shopping with a €500 note) and as long as the price to be paid is not more than €3,000.

They are, however, within their rights to refuse payment by card, or below a certain level, as is common in small shops. Cards and cheques, unlike cash, do not have to be accepted as payment as a matter of law.