I am afraid nothing earlier is available for Saulxures. But it seems that the parents of both Nicolas Strasbach and Catherine Gérard came from other villages, according to this well-sourced Geneanet tree: Ban-de-Sapt (10 km west) and Anould (30 km south-west), both in Vosges and with older records.
As the marriage record does not name parents, there is no formal proof that they are actually their parents. In the case of Catherine Gérard, it is very likely as she would then have sisters Barbe Gérard and Marie Gérard, who appear as godmothers of her children. In the case of Nicolas Strasbach it is less obvious, but there is a burial of a Jean Strasbach in Saulxures who could be his father.