It means "my little" as in "my little one".
my boyfriend is called "mon petit ami" or "mon ami" in French
It means "my little rascal" in French.
French-masculine > "My Small (or little) Family"
"le petit-fils de mon père est mon (fils // neveu)" in French means 'the grandson of my father is my (son // nephew)' in French.
It translates to "I love my little vampire" in French.
Mon petit tresor
toujours dans mon propre petit monde means 'always in my own small word' in English.
mon petit ami
"mon petit chaton"
The French expression is "mon petit chou", meaning literally "my little cabbage". Naturally this hasn't rally to do with vegetables, but is a pet name for someone you love, your partner or child.
j'aime mon petit chien, j'aime mon chiot.
"Envolez-vous mon petit oiseau" or "Envole-toi, mon petit oiseau"