Formal:
* Mon cœur est brisé. (This is the most literal translation and sounds very formal.)
Informal:
* J'ai le cœur brisé. (This is the most common way to say it and sounds more natural.)
* Mon cœur est en mille morceaux. (This means "my heart is in a thousand pieces" and is a more poetic and dramatic way to say it.)
More specific:
* Je suis dévasté(e). (This means "I am devastated" and conveys a feeling of deep sadness.)
* Je suis anéanti(e). (This means "I am annihilated" and conveys a feeling of complete despair.)
The best way to say it depends on the context and the emotion you want to express.