The pair, who are originally from the Isle of Wight, were due to travel back from France on Friday.
French media reported that an investigation has been launched into the death and that a post-mortem on the woman, believed to be in her 80s, took place on Friday.
Prosecutor of the Republic of Boulogne, Pascal Marconville, told local paper Le Journal Du Centre: "It was at the moment where they had to get out of the vehicle that the son realised she had died.
"She died because of her age and a cancerous pathology which could explain the marks found on the body, which are in fact bruises.
"According to the son, it would be linked to recurring falls."
Local police said that nothing suspicious was found at any of the three properties belonging to the pair.
A spokeswoman from the Foreign Office said: "We are aware of the death of a British woman and the arrest of a British man in Calais. We are liaising with the French authorities."
The son is reported to have been taken to a hospital in Calais.