The verb vouloir can be followed by either a bare infinitive or a noun phrase.

• que voudriez-vous boire?
• que voudriez-vous manger?

In these sentences, there is no preposition before “boire” and “manger” because they are the complement of the verb vouloir.

• Je voudrais quelque chose à boire.
• Je voudrais quelque chose à manger.

In these sentences, vouloir is followed by the noun phrase “quelque chose,” which functions as the direct object of the verb. The infinitive “boire” or “manger” does not function as the complement of vouloir. Instead, the infinitive modifies this noun phrase. After the phrase “quelque chose,” we introduce an infinitive using “à.”

Generally speaking, whether to use a preposition before an infinitive (and if so, which one) doesn’t depend on the identity of the infinitive, it depends on the structure and identity of the other related words in the sentence. We do use “à” after some verbs, such as “continuer”. But after other verbs, such as “décider,” we use “de.” And there are other verbs like “vouloir” that use a bare infinitive. An infinitive can also come after an adjective or noun phrase; in this case, the choice of preposition depends on the identity of the adjective or the noun phrase. You have to memorize which preposition goes with each structure.

Le ”à” avec son accent grave indique un rapport à quelque chose, un lieu, un objet, une idée etc…Je vais à Paris, je pense à ma maman, je joue à un jeu!