The 29-year-old, identified in the Indian media as C Thirumuguran hit the Frenchman in an argument that broke out while they were drinking, according to reports.
"The student got frustrated and hit him on the head with a wooden stick and he [the tourist] collapsed," senior police officer Senthil Kumar told the AFP news agency.
Thirumuguran then panicked, chopped up the body, tried to burn it, stuffed into a sack and dumped it in a canal, according to the Devdiscourse website.
Indian media have given two different identities for the Frenchman, whose passport is reported to have been in his suitcase, which was found by local people.
Thirumuguran's name was mentioned in a diary that was also in the suitcase, leading to his arrest and confession after being questioned on Sunday night, according to the Hindu newspaper.
The killing took place in Thanjavur, a district known for its temples, including the 11th-century Brihadeeswara Temple which is famous for its frescoed interiors.
Gay sex is illegal in India under British-era legislation that describes it as "carnal intercourse against the order of nature" and allows for jail terms of up to life.
The law is currently being challenged in the country's top court.