In French, you will never see an apostrophe "s." Possession is shown in a couple of different ways. One way is to use the preposition de (of) when you are expressing the possession in third person.
Example: le livre de Paul (Paul's book)
Another way to show possession is by using "possessive adjectives." Possessive adjectives are used to either establish a relationship between people or things, or to indicate that something belongs to someone. Read the sentences below and note how the possessive adjectives (mon, ma, and mes) are used.
C'est mon chat. = This is my cat.
Ce n'est pas ma tante. = This is not my aunt
Ce sont mes cousines = These are my cousins.
Note how the possessive adjective work? Just like an article! Identify the number and gender of the noun and add the correct possessive adjective. Voilà!