Two men, believed to be the assailants, held members of the congregation hostage for an hour before being shot dead by police after emerging on to the courtyard of the church in Normandy, according to local reports.
French newspapers suggested that the dead man was 92 years old and had served the community of Saint-Etienne-du-Rouvray, south of Rouen, for decades.
Police sources were quoted as saying that at least one of the two hostage-takers was bearded and was wearing a skullcap of the kind worn by some Muslims.
French president Francois Hollande and interior minister Bernard Cazeneuve are on their way to the scene.
The French government said one hostage was killed and another seriously injured.
One member of the congregation - made up of two nuns and two worshippers - was said to be seriously injured.
Pope Francis has expressed his "pain and horror" at the incident.
Vatican spokesman Federico Lombardi also added that the Pope was particularly appalled by the "barbaric killing" because it happened in a sacred place.
The French Prime Minister, Manuel Valls, echoed Pope Francis' sentiments, also declaring the the hostage situation a "barbaric attack".
"The whole of France and all Catholics are wounded. We will stand together," he said.
The hostage-takers entered the church armed with knives shortly before 10am local time, said French media sources.
As the situation developed, officers from the elite anti-terrorist Raid squad were called in to assist local police.
A number of shots were heard over a period of about 15 seconds as the incident came to an end around 40 minutes later.
Anti-terrorist authorities in Paris have opened an inquiry into the hostage-taking.
Eulalie Garcia, who works in a beauty parlour, is on the same road as the church, and told reporters that she knew the 92-year-old priest, who had taught her the catechism as a young girl.
"My family has lived here for 35 years and we have always known him," she said.
"He was someone who was treasured by the community. He was very discreet and didn't like to draw attention to himself."
She said she was very shocked by the death of the priest, who lived opposite his church.
with AFP
