Here's why and what it should be:
* "Les mois de" means "the months of" and is a starting point for a phrase.
* "sont" means "are" in the present tense, but doesn't make sense on its own in this context.
To make sense, you need to add the rest of the sentence:
* "Les mois de l'année sont..." ("The months of the year are...")
* "Les mois de décembre et janvier sont..." ("The months of December and January are...")
* "Les mois de vacances sont..." ("The holiday months are...")
Remember: French grammar requires a complete sentence, not just a partial phrase.