I believe P. domestica is a hexaploid species, while apricot is generally diploid. Therefore it is most unlikely that there are apricot genes in Mirabelle de Nancy. Not quite impossible. Apricot and P. domestica have both crossed with P. besseyi. But most unlikely.
Walter

Prunus domestica has been re-synthesized by crossing the diploid Cherry-Plum (P. divaricata) with the tetraploid Sloe (P. spinosa). The triploid offspring have low fertility but some of the F2 are fertile hexaploids.

I think it would be a fine idea to cross a plumcot (pluot, aprium) with an improved Sloe, aiming for a hexaploid that brings some apricot qualities into the P. domestica complex.

In the Rosaceae it is usually easier to make crosses if the parent with the lower chromosome number is used as seed-parent.

Karl