By Benoit Van Overstraeten and Leigh Thomas

PARIS (Reuters) -The biggest food industry companies in France have pledged to cut prices on hundreds of products from next month, Finance Minister Bruno Le Maire said on Friday, threatening financial sanctions if they break the promise.

The government is furious that prices consumers pay in supermarkets have hit record levels in recent months even though the prices industry pays for many raw materials have been declining.

Le Maire has previously threatened to claw back what he described as "undue" profits from food companies with special taxes if they did not pass on falling raw materials prices to consumers already struggling with high energy prices.

"As soon as July, prices of certain products will go down," Le Maire told BFM TV on Friday after meeting representatives of the food industry the previous day.

"There will be checks and there we will be sanctions for those who don't abide by the rules," Le Maire said, mentioning pasta, poultry and oil as some of the products on which prices will be cut.

While food inflation has become a concern for European governments from Britain to Italy recently, France has been among the most aggressive in pushing price cuts. In Hungary, Prime Minister Viktor Orban has imposed mandatory price cuts on some basic food items.

Le Maire said if the 75 food companies that make 80% of what the French eat do not live up to their promise he could name and shame them to the public.

"On a certain number of products where wholesale prices have fallen, then the (retail) prices will have to fall too, by 2, 3, 5, maybe even 10%," he said, adding that he would have the list of products concerned next week.

French annual inflation cooled more than expected in May to its lowest level in a year at 6.0% as energy and food price increases moderated. But food prices still were up 14% last month after a record spike of almost 16% in March.

Food prices surged after food companies and big retailers agreed in March to an average 10% increase in prices, responding to a surge in input prices the previous year and wages after Russia's February 2022 invasion of Ukraine.

However, the surge has hit the food-loving French's appetite as their spending on food, adjusting for inflation, has fallen to its lowest level since March 2009, according to data from the INSEE statistics agency.

Meanwhile, the food industry has seen profits surge, largely making up for sharp falls during the pandemic, Le Maire said. The industry's operating profits were up 15% in the first quarter from the previous quarter, according to data from INSEE.

(Reporting by Benoit Van Overstraeten and Leigh Thomas; editing by John Stonestreet, Silvia Aloisi and Hugh Lawson)