Sleepy:
* Fatigué (masculine) / Fatiguée (feminine) - This is the most common and general term for tired.
* Somnolent - This is more formal and literary.
* Endormi (masculine) / Endormie (feminine) - This literally means "asleep," but can be used to mean sleepy.
Tired:
* Fatigué (masculine) / Fatiguée (feminine) - As mentioned above, this is the most common and general term for tired.
* Épuisé (masculine) / Épuisée (feminine) - This implies extreme tiredness or exhaustion.
* Las (masculine) / Lase (feminine) - This is a less common word for tired, but can be used to express a feeling of weariness.
You can also use expressions like:
* J'ai sommeil - I'm sleepy
* Je suis crevé - I'm dead tired
* Je suis épuisé(e) - I'm exhausted
The best way to choose the right word depends on the context and the level of tiredness you want to express.