We had our co-ownership regulations amended by a law firm. Are we required to use a notary to have them registered with the land registration service?

Yes. “Any instrument or right must, in order to be subject to land registration formalities, result from an instrument executed in authentic form by a notary practising in France […]”. As the co-ownership regulations (or any amendments thereto) must be registered to be enforceable, they must therefore be drawn up in the form of an authentic instrument (Decree No. 55-22 of 5 January 1955, Art. 4).