Here is a concrete example. According to economic theory, the competitive price of a good in a free market should be the marginal cost of the least efficient supplier in that market. If a tax increases your costs but you are (still) not the least efficient supplier, then prices should not change at all, and the taxes will entirely come out of your margins.
This tax is aimed at a handful of large internet-only businesses doing business in France. These businesses are large and profitable in part because they operate very efficiently, and are in competition with offline companies whose operating costs are much higher. It is unlikely that this tax will by itself make their margins higher than the competitors, and therefore is unlikely to make them raise their prices.
What is an interesting scenario, though, is that taxes + GDPR fines + complying with new copyright legislation + whatever else gets dreamed up becomes enough that internet companies decide that it is worthwhile to take a stand and exit various EU countries. They haven't for a variety of reasons (including that corporation vs country battles can make other countries wary of said corporation), but if France keeps picking a fight, those calculations could change.
One of the upcoming interesting battlegrounds along this line is from recent EU copyright legislation. It strongly implies that various tech giants will be required to put software chosen by various national governments on their network to proactively identify and block copyrighted content. Software out of their control that processes everything coming in and has legitimate reasons to "phone home". Maybe you trust countries like France and Germany to only require trustworthy software. But what about more corrupt countries like Romania? Do you trust their copyright filter software to not cross the line into spying and censorship?