These rules, already in place in some areas, will be rolled out across France, Minister of Ecological Transition Agnes Pannier-Runacher told the Journal du Dimanche newspaper.
Energy costs in Europe have spiralled since the Russian invasion of Ukraine.
Shops will be fined up to €750 (£640) for breaking the air-conditioning rule.
Leaving doors open when air conditioning is on is “absurd”, Ms Pannier-Runacher told local radio station RMC.
She will issue two decrees on energy waste in the coming days, she told the Journal du Dimanche.
“The first will widen the ban on illuminated advertising, whatever the size of the city, between 01:00 and 06:00,” she said.
“The second will ban shops from having their doors open while the air conditioning and heating are working.”
The ban on neon signs is already in force in areas with a population under 800,000. Airports and stations are exempt.
Shell has warned energy rationing cannot be ruled out in the EU, as the region struggles to cope with disruption to gas supplies from Russia.
France continues to experience extreme hot weather, increasing demand for air conditioning.