"She had a great life. Mitzie Vern, Grandma. Just the best," Franco, 38, wrote while paying tribute to his grandmother.
He also posted a photo of himself with his grandma.
Vern died on Sunday in Cleveland, just about one month short of her 94th birthday.
While she was certainly best known as the grandmother of both Francos - James and his younger brother Dave - she did enjoy her time in the spotlight when she starred in a "Funny or Die" skit, criticizing anyone who did not see James' film "127 Hours".