An accident is something that didn’t mean to happen, or something that results in injury, possibly death. So when you talk about it in English in relation to social availability it sounds very wrong.
If you want to ask if someone doesn’t have any plans at late notice, you can’t say, „Are you accidentally free?“ because it’s no accident that the person is free, they may have simply not wanted to plan anything that evening.
So, better is to say something like, „Do you happen to be free on Friday night?“ or use the phrase ‚by chance‘, e.g. Are you, by chance, free on Friday night?
