Yes, Luis Alfonso's mother, Carmen, is a maternal granddaughter of Franco. King Juan Carlos has frosty relations with L-A and his family partially because
1) JC supports the Orleans branch as claimants to the French throne
2) L-A signed his name as Anjou (as in Duke of Anjou), a title which has been a point of contention between the Legistimists and Orleans pretenders.
3) After Carmen married L-A's father, JC and Sofia had to be extra nice to the couple (even though Franco had already named JC as the next king) for fear of upsetting Franco.