Well if she was being seriously considered by Alexander III and Marie Feodorovna then the Comte de Paris would have no doubt have been consulted. I can't imagine that the Emperor and Empress would do all that work, convincing Nicholas to marry Helene only for it to fall thew because of religion. Remember that Russia and France were very close ally's at the time so perhaps the Comte would see the benefits of such a marriage, especially if the French Republic unofficially supported the match. Maybe a deal, with Helene marrying Nicholas and the French revoking the Royal exile law?
Yes, he would've been consulted. Mostly because royal marriages were more political than anything and despite the House of Orléans having been off the throne since 1848, they were still royalty. That is the big thing to keep in mind: just because they formally occupied the French throne doesn't mean such a marriage would improve relations with France. The Orléanists lived in England, and I daresay the French Republic would probably not care at all. There was a flush of royalist sentiment following the collapse of Napoleon III, but it quickly turned to Republicanism when the Comte de Chambord remained intransigent over the flag.
Helene's father could probably see the benefit to such a match, but only one way: that is might be a step towards his restoration to the throne. After all, Chambord is long dead and there were no longer two competing factions for the French monarchy; most of the Legitimists quickly turned to support his candidacy following Chambord's death, with only the most reactionary, the
Blancs d'Espagne refusing to recognize the Comte de Paris as their King and instead proclaiming that it was male Branch of the Spanish Bourbons, who were also the Carlist pretenders, were King of France.
The marriage wouldn't impact the French Republic's relationship with Russia, but I doubt they would see any benefit from their end. Sure, a member of the Orléans family is Empress of Russia, but I don't see her having any pull towards France. Why push Russia further towards a path with the French when her own family is barred from setting foot in the country.
However, given that the match was one approved of by Alexander III and Marie Feodorovna, it does have a better shot. Her father and the Pope may of objected to a match with Britain because the conversion meant becoming a Protestant. Her grandfather, the Prince Royal Louis-Philippe had been married to a Protestant with no fuss, so perhaps that is why the French Pretender balked at the idea of his daughter having to convert.
The big issue is Alexandra. As long as Nicholas is infatuated with her, he's not going to consider Helene or anyone else. There is also the big problem as Helene herself wasn't interested in the match: I think she was considered by the Emperor and Empress, but nothing formal ever began, with the big reason being that she did not want to convert to Russian Orthodoxy. Her being in England meant she had lots of contact with Prince Albert Victor and they fell in love, hence her offering to convert.
You just need a POD that will make Nicholas want to be with Helene; after all, even Alix refused at first over the religious issue but ultimately consented to marry him as she'd grown to like him. Perhaps if the 1886 banishment law is never passed, the Orléanists remain in France. That'd also free Helene from the mind of the English Prince. It'd also be a way for the Republic to see benefits, especially if the Orléanists are politically and socially active within the country, although it's hard to create an atmosphere where the Republic
doesn't want to banish them.
A restoration of the monarchy would also make this much more possible, if Chambord died early enough before the Royalist Parliament turned Republican. Or perhaps with no banishment law something could occur with Boulanger although he was an opportunist and pretty much courted all of the royalist factions for support.