French businesses still pay VAT on stuff they buy from other companies.
Generally, most VAT systems work this way: Business collects VAT from customers for services or goods sold(output VAT), and must pay it to the government. But businesses may offset that liability with the VAT they paid acquiring goods or services that were used in their own revenue-generating activities (input VAT).
So, for example, ACME sells TNT for $10 and VAT is 10% or $1 (output VAT), so price to customer is $11 and ACME's VAT liability is $1. Say ACME paid $0.25 VAT to its suppliers for the chemicals in the TNT and the paper casing (input VAT). ACME's net tax liability is $0.75, and that is how much they would actually fork over to the government.
Note that if ACME's customer is Bugs' Mining Shop, i.e., a business, they still charge VAT on the transaction.
In a sales tax system, ACME would not have paid sales tax to its suppliers at all, and it would not have charged Bugs' Mining Shop a sales tax. Thus, sales tax is generally more economically efficient than a VAT from a business perspective.