The ticket for my accident was reduced to a parking ticket. What will an insurance company see?

If it was reduced to a municipal parking ticket (not state or provincial, and not a moving violation of any kind), then no. Parking violations don't show up on an official driving record, only traffic convictions do. But make damm sure it really is just a municipal parking violation.

Whether you are convicted of anything in a court of law does not wipe out the fact that you had an accident. Insurers keep a database of claims, so if you insure your vehicle with a new insurer they can see that you had an accident on such and such a date because the insurer you had the claim with would have uploaded the information. What traffic violations you were convicted of within the last x number of years (typically 3) is a record that is maintained by the State.

They'd 'see' it as a parking ticket, so you're in luck !