250 riot police, known as the CRS, were on duty on Sunday night in the south-east city to prevent further trouble.
Problems started after police arrested a man on New Year's Eve who was reported to have attacked them.
After a chase the 30-year-old man was allegedly thrown to the ground and handcuffed. He fell into a coma after suffering a heart attack while being taken to a police station.
Angry youths have staged repeated protests about the attack since then, culminating in cars being burnt on Friday and Saturday night.
Newspaper France Soir reported that the local police chief was determined to keep calm in the city.
Francis Lamy said he would "not allow any no-go areas in Clermont-Ferrand."
Police have been dealing with groups of young people moving quickly around certain districts of the city.