Learn French: Ce bébé a seulement un an. - This baby is only one year old.

In English, you "are" an age, but in French, you "have" years. The word a is the "he/she/it" form of avoir (to have). So literally, this sentence says "This baby has only one year."

Is the word bébé always masculine, even if the baby is a girl?

Yes! The noun bébé is always masculine, which is why we use the masculine word ce (this) in front of it. You use ce bébé regardless of the actual child's gender.

Could I say cet bébé instead of ce bébé?

No, you must use ce. Both mean "this", but ce is used for masculine words starting with a consonant (like bébé). You only use cet before a masculine word if it starts with a vowel or a silent 'h' (like cet enfant).

I've also learned the word année for year. Why do we use an here?

When stating an age with a number, you always use an (for one year) or ans (for multiple years). The word année is used when talking about a year as a block of time, like wishing someone a good year (bonne année).