if the word 'chienne' means also '❤❤❤❤❤' in French, this sentence may be considered like: this is my male ❤❤❤❤❤, how to say male ❤❤❤❤❤ in English? Then, i've just found the appropriate word for French. :)
Why is it "he is my dog?" "C'est" is used instead of the possessive right? So how do you know if it's going to be "She is my dog" or "He is my dog"?
'chien' is the word for male dogs, and 'chienne' is the one for female dogs. Also, 'mon' refers to a masculine noun, if it was a feminine noun following it, it would be 'ma'. Hope it helps ;)