Oh wow, I never even considered the salt itself would be an issue. It looks like you would likely have coarse grey salt, gros sel, as your large grain salt? I use Kosher or coarse sea salt, which from what I can find, is fairly the same volumetrically, but things also said grey salt is denser with actual salt. The saltwater is pretty much a saturated solution or close to it, so I don't know if you could actually oversalt the water. The weight ratios I found have around 1 lb salt per 4 lb potatoes.
For the potatoes themselves, we have little bags of boiling potatoes, either white, red, or a mix or red, white, and purple. They have thin skins and hold up well for boiling. Looking up French styles, la Charlotte, Ratte, l'Amandine, Belle de Fontenay, Annabelle, Franceline, Nicola, Roseval, and Chérie all seem likely useable. Ours are around the size of a golf or ping pong ball. All yours seem more finger shaped so I can't tell exactly how large they are.
Maybe you can find a French recipe for the papas arrugadas the other commentor mentioned to get a version with things you can buy more easily. Other than the sauce, the idea seems the same.