The 68-year-old's body was found packed into three sandbags in Tamil Nadu state's Thanjavur district on Sunday.
A 29-year-old student, who has been arrested, confessed to killing the Frenchman in an altercation after the pair had sex, senior police officer Senthil Kumar told AFP.
“The student got frustrated and hit him on the head with a wooden stick and he (the tourist) collapsed,” he said.
Kumar said the French embassy in New Delhi had been informed of the murder. An embassy spokesman told AFP he was not immediately able to comment.
Local and foreign tourists flock to Thanjavur for its myriad temples, including the 11th-century Brihadeeswara Temple famous for its frescoed interiors.
India bans gay sex acts as “carnal intercourse against the order of nature” and allows for jail terms up to life under British-era legislation that is currently being challenged in India's top court.