Compliments of BBC
The two attackers, who said they were from the so-called Islamic State (IS), slit Fr Jacques Hamel’s throat during a morning Mass, officials say.
Police later surrounded the church, in St-Etienne-du-Rouvray, and shot dead both hostage-takers.
One of the hostages is in a critical condition in hospital.
President Francois Hollande, visiting the scene, said the attackers had committed a “cowardly assassination” and France would fight IS “by all means”.
Pope Francis decried the “pain and horror of this absurd violence”.
One attacker is reported to have been known to French police, and had tried to enter Syria last year.
Police special forces raided a house in Saint-Etienne-du-Rovray in the aftermath of the attack, and French prosecutors earlier said one person had been arrested.
The attack happened during morning Mass at the historic church, situated in a quiet square of St-Etienne-du-Rouvray.
One nun who witnessed the attack, told BFM TV that the men forced Fr Hamel to his knees and recorded the killing, speaking Arabic as they did so. She says she fled as they were preparing to kill him.
Elite police units, specialised in hostage-taking, surrounded the church.
President Hollande said the attackers claimed to be from the self-styled IS before they were killed by police as they came out of the church.
Three of the hostages were freed unharmed, but one remains in a critical condition, said French interior ministry spokesman Pierre-Henri Brandet