Jacqueline cleaning the cuts on Danielle's back after the latter was whipped, while agreeing that Marguerite deserved the beating she got.
The prince came to rescue Danielle, after he had horribly rejected and humilated her at the ball. To his surprise, she had already rescued herself. He then apologized to her, admitting that he was wrong and he betrayed her trust. But it turns out that she had already forgiven him for it.
Prince Henry (in apologizing for being a Jerkass) spontaneously calls Danielle by her real name (instead of Nicole, her mother's name, which he has been using up this point). She begs him to repeat not the apology, but the part where he says her name.
Another Heartwarming Moment came when he finally proposed to her.
"I kneel before you not as a prince, but as a man in love... But I would feel like a king if you, Danielle de Barbarac, would be my wife."
While it doubles as a Funny Moment because of its over-the-top nature, the wedding scene between Henry and the Spanish Princess Gabriela. She's sobbing uncontrollably, begging her parents to let her marry her lover, a commoner. Henry is kneeling at the altar seriously, and then, all of a sudden, bursts out laughing at the absurdity of it all, and despite the language barrier, he calls off the wedding and lets her to go her lover.
This troper found it heartwarming that Jacqueline was able to find love at the ball (she and Laurent hit it off), even after her mother spitefully told her, "You're just there for the food." This scene may have led to Jacqueline deciding that she deserved better than being The Unfavorite, prompting her to turn against her mother.
Da Vinci encouraging Danielle to go to the ball and tell Henry the truth wins Heartwarming points:
Danielle: A bird may love a fish, signore, but where will they live?