France has begun a new chapter in the saga of its online book wars, with French MPs unanimously backing a move that will curb the discounting power of Amazon in the country.

Warning that small independent bookstores were facing unfair competition from the US internet firm, MPs supported a bill that will prevent it combining free delivery with 5% discounts on books.

In a rare show of unity, parliamentarians on the right and left voted for the move to defend the French "cultural exception" against market forces and global digital powerhouses.

The bill, which must now be approved by the senate, is the latest round of French politicians taking on the might of the major US internet firms.

Since 1981 French law has fixed book-prices so that readers pay the same whether they buy online, from a big high street chain, or from a small bookseller. Extensive discounting is banned.

The government said the measure has saved its independent bookstores from the ravages of free-market capitalism that hit the UK when it abandoned fixed prices in the 1990s. The law, which applies to all online booksellers, does allow for a small amount of discounting – as long as it is no more than 5%. Small booksellers argue they cannot compete with Amazon because it provides free postage and free fast delivery deals on top of 5% discount.

The culture minister, Aurélie Filippeti, who backed the bill, had told booksellers in a speech in Bordeaux last year: "Everyone has had enough of Amazon, which by dumping practices, slashes prices to get a foothold in markets only to raise them as soon as they have established a virtual monopoly … the book and reading sector is facing competition from certain sites using every possible means to enter the French and European book market … it is destroying bookshops."

Guillaume Husson, of the booksellers union, Syndicat de la librairie française, hailed the bill as a sign that public powers were "putting some balance back into the conditions of competition".

There are between 2,500 and 3,000 independent bookshops in France, compared with under 1,000 in Britain. Around 500 of the French independent bookshops sell online but they have warned that they were unable to compete with Amazon.

Romain Voog, head of Amazon France, said in Le Figaro that the bill went against the interest of consumers and would push up the online price of books compared with prices in bookshops.

"Numerous customers live far from any bookshop and appreciate being able to buy their books online," he said, adding: "If this bill passes, it will have a minor impact on Amazon but it will penalise consumers and threaten cultural diversity in France because Amazon offers the biggest choice of new and secondhand books in France."

Voog said the company's four vast new warehouses in France stocked 800,000 titles, and offered books published more than a year ago while smaller sellers focused on new releases.

In recent years the French government has taken on a number of US internet and tech firms. Investigators are looking at the terms of Apple's contracts with mobile operators and last week the French data-protection watchdog threatened action against Google for failing to comply with national privacy guidelines.