Yes, this sentence makes sense if French.
That means the person has been controlled by the police, likely at a DUI control point and is over the BAC (Blood alcohol content) legal limit which is 0.5 g of alcohol per liter of blood in France.
As the translation attempt is “he drinks too much”, I assume the context is about someone, not something.
However, Antoine’s answer rightly states il might also refer to things, maybe a baba au rhum that contains too much alcohol, or a wine. In such cases, “il a un taux d’alcool trop important” is still possible but we are more likely to say il contient trop d’alcool for the former or son degré est trop élevé for the latter.
In french, “taux” means “grandeur exprimée en pourcentage ou proportion” which could be translated to “how big or important something is in percentage or proportion”. It’s implicit that “taux d’alcool” (alcohol level) is about his body, because there is nothing else that could mean.
In the sentence, “il a un taux d’alcool trop important”, it is implicit that the alcohol level of his is about himself, his body, his person.
You could say the same sentence about a drink. “il” could also be a drink, for example.
Hopefully it is not more confusing than it already was. But yes, I can understand why it is confusing because the expressions are used very differently in french and english.