French adverbs indeed “may modify verbs, adjective, prepositions, or other adverbs”.

• Paul a beaucoup mangé.
• Paul est très content.
• Paul est exactement devant chez toi.
• Paul est très très énervé.

A lot of the “adverbs” cited on your referenced page are not actual adverbs: Pro-PP (e.g. ici, là, maintenant, hier, dehors), Pro-clitics (en, y), Pro-QU (e.g. combien, comment, où, pourquoi, quand). And others are adverbs which can take NP/noun compléments with the de preposition (e.g. beaucoup, assez, peu). Finally while moins and plus are adverbs, le moins et le plus are not words and hence are not adverbs. Lexical grammatical categories being appropriate only for words.