Constantine wasn't all that important. He was pope from 708 to 715 and was remembered as "a remarkably affable man," but he's mostly forgotten now, even though the Emperor Justinian II treated him with honor when he visited Constantinople. He resisted the next emperor's attempt to revive the Monothelete heresy.
In the 3rd century there was a dispute at Antioch with two men both claiming to be the rightful bishop. The emperor Aurelian decided to recognize as legitimate the one accepted by the bishop of Rome. That shows that the pope's influence doesn't start with the emperor Constantine. Aurelian was a pagan but got called on because there was property at stake in the dispute.
I believe that Republic of Maine was referring to the Emperor Constantine - 306 Constantius died, and his son Constantine was proclaimed Emperor of the West by his troops even though Maxentius was still the Caesar of Italy and Africa. - and not the Pope named Constantine 402 years later.