The investigation follows a recommendation from the French anti-fraud office and will be run by public health magistrates, they said.
France is already investigating global heavyweight Volkswagen and French champion Renault for allegedly fitting engines with devices designed to fool emissions test equipment, making cars seem less polluting than they actually were.
US-Italian owned Fiat Chrysler is one of the world's top 10 carmakers.
It is already being accused in the United States of emissions cheating. The US Environmental Protection Agency said the undisclosed software on the 2014 to 2016 models of Grand Cherokees and Dodge Ram 1500 trucks sold in the US allowed the vehicles to emit more nitrogen oxides than permitted.
The company said its bottom-line net profit soared to 1.8 billion euros (USD 1.9 billion) in 2016 from 93 million euros a year earlier.