I feel like Croix and Chariot in the past, did date for a considerable amount of time. No doubt it would most likely be an on again off again kind of relationship, but it's strongly implied from the flashbacks that they were romantically linked. This is evidenced by the fact that Croix was backstage after Chariot's performance when she used the Dream Fuel Spirit without knowing what it really did. Croix being backstage meant two things: One, that she had such strong relationship that she could be in her dressing room after the show, and two, Chariot trusts Croix alone in the dressing room.
Another way their relationship is strongly implied is when they were talking about what they were going to do with the Grand Triskelion in the flashback, how Croix reacted when she was chosen instead of her. Sure, a first she was angry because she wanted to be the one to open the Grand Triskelion, but after Chariot started crying, she softened. She went up to Chariot and hugged her, all the while saying that she should take this as a blessing and that is was okay for it to pick Chariot over herself.
Another way their relationship is strongly implied is the second to last scene in the two seasons of the show. It shows Croix getting taken away to a rehabilitation place or somewhere to help her not do something evil again, but then saying she will find the cure for Wagandea for Chariot. After learning this, Chariot is astounded to the point where she can't speak until Croix leaves to the Leyline. Then Chariot calls out into the air "Croix! Come back soon, okay? I'll be waiting...". Meaning, she wants to see Croix again, and that she can't wait until they meet again, which is very similar to what couples say in movies when parting.