It is the latest move by the government aimed at bringing down the number of road deaths caused by alcohol.
All motorists must also have with them a high-visibility safety vest and a warning triangle.
Foreign drivers are included in the new rule, however there is a grace period until November.
Some 4,000 people are killed on French roads every year, with drink-driving being the main factor in accidents ahead even of speeding.
Bonanza for manufacturers
The French government hopes that with breathalyzers in every car, drivers who suspect they may be over the limit can test themselves and if necessary refrain from taking the wheel.
The former government of President Nicolas Sarkozy, which gave the go-ahead to the new law, said it hoped 500 lives might be saved every year.
Motorists driving without the two breathalyzer tests will be handed a fine of 11 euros under the rules, which exclude mopeds, drivers who fail to produce a breathalyzer after 1 November will face a fine of 11 euros.
The kits come in two types: expensive electronic ones which can be reused; and cheap chemical ones, says the BBC's correspondent in Paris.
Tens of millions of the kits are going to have to be supplied, but right now there is a shortage, which is one reason for the four-month grace period.
He adds that the new rule is proving a bonanza for manufacturers, of which there are only two in France.
Meanwhile, drivers' groups opposing the measure say it has been foisted on France by clever industry lobbying.
To enforce the regulations, French police say they plan to carry out random checks on those entering the country through the Channel Tunnel, as well as drivers arriving on ferries.
Retailers in Britain say sales of breathalyzers have risen considerably due to the law, the Press Association reports.
Car accessory retailer Halfords said there had been unprecedented demand, but said that 6 out of 10 Britons travelling to France were not aware of the changes.
The drink-driving limit in France is 50mg of alcohol in 100ml of blood - 30mg less than the UK limit.