Deaths rose 29% in the last week of June compared to the week before, with French health minister Stéphanie Rist adding there had been a "clear increase" in deaths among those over 45.
France saw its hottest day ever on average country-wide on 24 June, with temperatures hitting almost 41C in Paris and half the nation placed under a red heat alert.
News of the death toll comes with parts of Europe, including the UK, braced for more searing temperatures from this weekend.
