This is because French has silent "h" - words that begin with "h" are not considered aspirated and don't behave like words starting with a vowel.
If you're looking for adjectives that start with "h" in French, you might be thinking of words that have an "h" later in the word, like:
* heureux (happy)
* honnête (honest)
* habituel (usual)
* haut (high)
Let me know if you'd like to explore other types of French words or if you have any other questions! 😊