Bonjour Laura,

This type of question has been discussed many times on this Forum

https://progress.lawlessfrench.com/questions/view/i-m-confused-here-why-j-ai-faim-but-not-je-suis-faim

The above link is just one out of many on the subject.

I hope that you will find the answer to your query by studying the link contents. 

Bonne continuation,

Jim

Since faim is the noun "hunger" and not the adjective "hungry" in French. So you say "I have hunger". 

When you use J’ai versus Je