Regardless of whether there are better ways to form this sentence (and most definitely shorter) I want to know if its grammatically correct. I know "fortunate enough to" is possible (He was fornunate enough to win the lottery) but is this as well or does it sound weird?
If you think he was unfortunate to the degree that he was involved in a car accident, then go ahead with your sentence; it's grammatical. But if you mean he was fortunate to the degree that he was not involved in a car accident, then your sentence is not correct. Instead, you should say:
He was fortunate enough not to be involved in a car accident.
I found an example sentence similar to yours on the Merriam Webster dictionary website:
"She was unfortunate enough to have been chosen as an example."
So, I think it's safe to say that it's a grammatically sound sentence. I don't think any English speaker would have a problem understanding what you're saying.