The man was arrested in Toulon after a severed head was found in a cardboard box that had been thrown out of a window of a flat.
There are fears of a renewed US-Iran clash a year after the US drone killing of the Revolutionary Guard chief, in the dying days of Donald Trump's presidency.
Authorities say the mother of the three girls and two boys aged between one and eight is suspected of killing them.
The 35-year-old suspect was allegedly asked by a father not to blow smoke in his children's direction, and then plowed his car into the family.
Divers on Friday pulled the last bodies from the wreckage of a “duck boat” that sank a day earlier during a storm in a lake near a popular Missouri destination, killing 17 people in one of the deadliest US tourist incidents for years.
Filipino mayor Antonio Halili was killed during Tanauan City's weekly flag ceremony on Monday.