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Since your card is French, it will not incur these fees.
Merchants in Denmark often apply fees (or up to several percent of the sticker price) to payments with cards issued outside the EU, but they are forbidden from doing this for consumer cards covered by the Payment Services Directive II. These rules do not distinguish between Danish and other EU cards.
These rules were introduced in January 2018, so if your guidebook is older than that it might be speaking about the previous situation.