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Going off what you said to Roxstar about her background, it sounds like she might take after mother, who must have been a bit of a wild card to have a baby and either refused to name the father or not know. I'm going to imagine the mom like Meryl Streep's character in "Mama Mia" but with French ancestry. I can see the Mom liking Madeline, so that works.
Other ideas:
Adeline
Carmen
Céline
Celeste
Chloé
Danielle - This would be an interesting choice on the mother's part due to the meaning, God is my judge, which sort of implies that God can judge her but not others.
Emma
Eve
Geneviève
Giselle - The meaning is odd, but maybe her mom felt tied down by a baby.

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As an aside, I wonder if people around her would see the character as sweet. From an authorial perspective, you have insight into her intentions, but other people would go off of what she says and her actions/inactions. People who habitually don't think before they speak are often not thinking of others. Free-spirited and spontaneous is sometimes code for someone who is unreliable, frequently keeps others waiting, and doesn't plan ahead. What does "not liking to be controlled" look like in her life? Is she a commitment phobe? Is she a rebel for the sake of it? Maybe there is a gap between how she sees herself and how she comes across to others.