I was curious so I went to the site:
https://www.dmv.ca.gov/portal/vehicle-registration/new-registration/register-your-boat-vessel/
"If you own a sailboat over eight feet long
or a boat/vessel with a motor (no matter the size), you must register it with DMV in order to legally operate it on California waterways."
I am guessing that if the Canoe never had a motor on it, there is no reason why it would be registered.
"A documented boat/vessel is registered with the U.S. Coast Guard and has a marine certificate. These boats/vessels do not have to be registered with DMV." Looks like if you can register it with the Coast Guard you don't need to fool with the DMV.
"An undocumented boat/vessel is registered with DMV and does not have a marine certificate from the U.S. Coast Guard.
If you buy a new boat/vessel, it is automatically considered undocumented, so you have to register the boat/vessel with DMV before you can put it in California waters."
If you don't mind a white lie. Someone left a Bicycle in my yard. I turned it into the Police lost and found and after the time period when someone got to claim it and it was unclaimed I went back and I owned it. There must have been some paper work on that.
Don't know how the lost an found thing works with boats/vehicles. But, if it is the same you will end up with paper work saying it is yours.