Yes. An acknowledgement of debt may be executed as a private deed if it states the amount of the debt in figures and words and bears the signature of the person undertaking the obligation (French Civil Code, Art. 1376).
It may also be drawn up as an authentic instrument. A notarised deed then gives the acknowledgement enforceable status, allowing the creditor to pursue the debtor in the event of non-payment without having to apply to the court.
Whether executed as a private deed or an authentic instrument, it must be declared to the tax authorities when the amount is €5,000 or more (French General Tax Code, Annex III, Arts. 49 B and 23 L).