The victim, named as David Daniels, aged 72, was fatally shot outside his home at around 7pm in the village of Edon, in Charente, a small village of just 270 residents close to the border with Dordogne.
French prosecutor Jean-David Cavaillé told media at a press conference on Wednesday that two men, an 85-year-old and his son, aged 48 were arrested just two hours after the murder and have been placed in custody on suspicion of murder.
Edon. Map: Mappy
(The village of Edon)
The suspects are believed to be neighbours of Mr and Mrs Daniels, who owned a farm.
The 48-year-old son is believed to be the farmer who worked on the Daniels' land and was born and raised in the village. He is also being investigated for a violent attack on Mr Daniels in 2017, according to local press.
A hunting rifle was confiscated by police and is suspected of being the weapon used to shoot Mr Daniels.
Prosecutor Cavaillé said the murder may have been the result of a dispute over the lease of farm land and differences in opinion over the development of the land.
The Daniels owned 130 hectares including forest, grazing land and crops.
Another report in Sud-Ouest newspaper suggest the "cleanliness of the property" was the source of the long-running dispute.
Mr Daniels was killed as he took his refuse bin outside his property, but prosecutors refused to say if he had an altercation with the suspects at this point or the shooting was planned.
He was driven by his wife to a doctor's surgery in Dignac (below), 12km away, but he died on the way. Gendarmes were called and immediately cordoned off part of the village.
Forensics teams were brought in to examine the scene.
One Dignac resident told Charente Libre: "I went to buy cigarettes just before 7pm. I saw a woman pulling one of the doctors from the surgery opposite to the tobacconist by the arm. We quickly realised something serious had happened.
"Gendarmes and firefighters arrived quickly. They told us later it had been a murder. We don't know who the victim is. It's very scary. A lot of people have locked themselves in."
The two suspects are due to appear before prosecutors on Thursday. An autopsy was also due to take place on Thursday.
The Daniels had lived in Edon for the last twenty years.
According to reports in the British press, they also owned a house in London where they spent part of the year.
Villagers in Edon spoke of their shock on Wednesday after the murder of Mr Daniels.
Mayor Patrice Petit said the death of Mr Daniels "was a big loss to the village."
"He was a man I knew very well, a man much appreciated in the commune where he had lived for a long time," said Petit.
"It's unacceptable, unacceptable," Petit told Charente Libre newspaper.
He told how Daniels had generously donated money for the upkeep of the heritage of the commune, a gesture he wanted to keep low key.
Mr Daniels collected classic cars and regularly took part in the classic car race in Angouleme known as the "circuit des Remparts".