There is plenty of parking in Downtown Oroville both street-side and in public lots. The following info is from the City of Oroville’s parking enforcement guide and subject to change.

On-street hourly parking is enforced Monday through Saturday
between 9:00 a.m. and 6:00 p.m. and is generally limited to 2 hours.
This parking limit is not enforced on Sundays and legal holidays.
All-day parking is permitted in certain portions of city parking lots.