Airlines don't ask about or research accident history. They will normally just look at the citation history. They wouldn't normally ask about the details of garden variety moving violations, but they would ask about reckless, and of course anything DUI related.
It's possible they might research your civil history, so they might find it if you got sued over an accident.
If your tickets were all garden-variety (minor speeding, ran a stop sign, illegal turn, etc) AND you were very young (teenage, or well under 25) you can likely overcome this if you keep your nose clean. But due to the history you need to drive like Mother Theresa, I mean ZERO infractions until you're off probation at your career airline. Then you can buy a maserati and go to town if you want. You also need to be able to explain what you learned and why you changed your attitude... they will need to believe it in their hearts, reckless is not a trait they're going to tolerate.
You also need to keep a clean record in all other things, since you effectively already have one "strike" with the airlines. And one or just maybe two is about all they tolerate (better majors).
Now if you got the tickets at a more advanced age, or you have more than maybe one reckless, it's likely to be harder...
Regionals will hire almost anyone. You'd be fine for that.
Lower-tier majors have already lowered their historical standards, with the looming retirements you'd have a shot there I think.
Top-tier will always be a bit more picky. Whether you have a shot there depends on the details, and how you address it at an interview.