If they were of French origin, their name likely was originally Pariseau, then shortened to Pariso when in the US. (I have French/Canadian ancestors who changed their spelling from Barbeau to Barbo, later back to Barbeau.)
There were several areas in Ohio where French/Canadian settlers lived, some in northern Ohio, such as Defiance, and Gallipolis on the Ohio River. French/Canadian voyageurs sailed the Great Lakes and the Mississippi and Ohio Rivers, among others, and there are persons named Pariseau in censuses in Wisconsin & Minnesota.
French-Canadian records, both civil and religious, are quite good, going back to the 1600s in many cases. Good luck.