I was wondering what familial line would be next in line as Princes of the Blood after the Bourbon family (both Vendôme and Montpensier branches), if you completely ignore that branch of the family. So not Condé or the like.
From what I have been able to suss out it would lead all the way back to Robert of Burgundy and the Afonsine line of the Portuguese house of Burgundy, with a departure from the Portuguese dynastic line in the succession crisis of the 1380s when the Avis came to power, though this really depends on whether you hold up Pedro I's marriage to Ines de Castro as backward legitimizing.
However, if you don't go that route or view them as illegitimate, who would have followed the Bourbon in the succession? I am having a hard time following the Portuguese lines of succession, but I am pretty sure the candidate would have been somewhere in there. I haven't been able to identify who else would have followed if not the Afonsines.