Hamel, 85, had his throat cut by two teenage jihadists, who took him and four others hostage in his church in St.-Etienne-du-Rouvray in northern France on July 26.
A large screen was erected outside the cathedral, where hundreds gathered in the rain to watch live footage of the proceedings inside.
"We're here as Father Jacques would have liked, together," Lebrun told the mourners, who included French Interior Minister Bernard Cazeneuve and former Foreign Affairs Minister Laurent Fabius. "Ready to commune more, attentive to one another, not excluding anyone."
Lebrun paid tribute to Hamel's 58 years of service as a priest -- a vocation to which he was "wholly devoted," he said.
He noted that Hamel's pursuit of his religious calling never took him far from the town of Darnetal where he was born -- just 8 kilometers (5 miles) from St.-Etienne-du-Rouvray.
"Jacques, you were a faithful disciple of Jesus," he said.
The priest's sister, Roselyne Hamel, recalled his military service in Algeria in his youth, during which he turned down a position as an officer because it might have required him to give orders to kill.
She said that once, during his service in Algeria, he had cheated death when he survived an attack that killed fellow soldiers.
"He would often ask himself, 'Why me?' " she said, explaining that God had chosen him for a life of service.
Lebrun extended his thoughts for the priest's family. "We only want to surround you this morning," he said.
He thanked those from other religious communities -- including Muslims and Jews -- whose attendance showed they had "decided to come together, so that this should never happen again."
On Sunday, Muslims attended Mass in churches around France and in neighboring Italy to pay their respects to the slain priest.
In the wake of Hamel's killing, an Italian politician, Lombardy President Roberto Maroni, called for the priest to be made a saint.
String of atrocities
The killing of the elderly priest in a house of worship rocked France, already stunned by a string of Islamist attacks, including one on Bastille Day in Nice that left 84 people dead.
The attack on the priest further strained religious tensions, and raised questions about the government's ability to respond to the domestic terror threat.
Both attackers -- who pledged allegiance to ISIS -- were known to security services. One of them, Adel Kermiche, 19, even wore an electronic monitoring device during the attack, officials say. He had traveled abroad to try to fight in Syria.
A source close to the anti-terror investigation told CNN on Monday that Kermiche and his fellow attacker, Abdel-Malik Petitjean, also 19, first contacted each other four days before the attack
via Telegram, an encrypted-messaging app that jihadists favor.
Kermiche and Petitjean, whom police shot dead as they left the church after the killing, carried out the attack in the name of ISIS.
On Sunday, the Paris anti-terrorism prosecutor's office said that Petitjean's 30-year-old cousin had been arrested and charged with having known the attack was imminent.
As part of its fight against radicalization, the French government said it has closed 20 mosques across the country since the November terror attacks in Paris
and plans to fund alternative Muslim places of worship free of extremist influence.
The burial of one of the killers has proved contentious, with Muslim leaders in the Normandy town where the priest was killed refusing to bury Kermiche
, according to the president of a local Muslim organization.