Beaucoup de citadins visitent cette galerie après le boulot pour se détendre.

After quantity expressions like beaucoup, peu, trop, assez, French almost always uses de (or d’), never des:

• beaucoup de citadins – many city dwellers
• peu de temps – little time
• trop de problèmes – too many problems

Des is the normal plural indefinite article (“some”) without a preceding quantity word:

• des citadins visitent… – some city dwellers visit…

Once you add beaucoup, it must be beaucoup de, not beaucoup des, unless you are specifying a previously mentioned group, which is rare and would sound very marked (e.g. beaucoup des citadins dont je t’ai parlé…).

With countable nouns, beaucoup de is almost always followed by a plural:

• beaucoup de citadins – many city dwellers
• beaucoup d’étudiants – many students

Beaucoup de citadin (singular) is grammatically possible but sounds wrong in normal speech; it would be understood as “a lot of city dweller,” which is illogical with a countable noun.

You might see the singular after beaucoup de with a mass/uncountable noun:

• beaucoup de travail – a lot of work
• beaucoup de bonheur – a lot of happiness

Citadins means “people who live in a city,” “city dwellers,” or “urban residents.” It focuses on where they live (city vs countryside).

Citoyens means “citizens” in the political/legal sense (having rights and duties in a state).

So:

• les citadins – urban dwellers (as opposed to people in villages or rural areas)
• les citoyens français – French citizens (nationality / legal status)

English “citizen” is often translated by citoyen, not citadin.

The subject is beaucoup de citadins. In French, a phrase like beaucoup de + plural noun is treated as a plural subject:

• beaucoup de citadins visitent – many city dwellers visit

So the verb must be 3rd person plural: ils visitent → visitent.

If the subject were singular, you would use visite:

• Un citadin visite cette galerie. – A city dweller visits this gallery.

No. In the present tense for ils/elles, the written ending -ent is completely silent:

• ils visitent → pronounced like [vee-zeeht] (approx.), same as il visite in sound.

So:

• il visite and ils visitent sound the same in speech; only context reveals whether it’s singular or plural.

Yes. In French, the present indicative is commonly used for:

• actions happening now, and
• habitual or repeated actions.

Here, Beaucoup de citadins visitent cette galerie… is understood as a regular habit:

• “Many city dwellers (regularly) visit this gallery after work to relax.”

If you wanted a future meaning, you could use the future:

• Beaucoup de citadins visiteront cette galerie… – Many city dwellers will visit this gallery…

Galerie is a feminine noun in French. The demonstratives agree with the gender and number of the noun:

• ce – masculine singular (ce musée)
• cet – masculine singular before a vowel sound (cet appartement)
• cette – feminine singular (cette galerie, cette ville)
• ces – plural (ces galeries, ces villes)

So it must be cette galerie because galerie is feminine singular.

Une galerie can mean several types of places, depending on context:

1. Art gallery – where art is exhibited and sometimes sold.
2. Shopping arcade / small indoor mall – a covered passage with shops.
3. Less commonly, other senses (corridor, tunnel, etc.) depending on context.

In everyday urban context with visiter and se détendre, it’s most naturally understood as either:

• an art gallery, or
• a shopping arcade / gallery in a mall where people stroll and browse.

Boulot is informal/colloquial French for “work” or “job.” It’s very common in spoken language and casual writing.

More neutral/formal options:

• après le travail – after work
• après le bureau – after (time at) the office

So:

• après le boulot – relaxed, everyday register
• après le travail – neutral, fine in most contexts

You generally need the article here:

• après le boulot
• après le travail

Dropping the article (après boulot) sounds wrong in standard French.

French normally uses an article with generic nouns like le travail, l’école, le bureau in such time expressions:

• après l’école – after school
• avant le dîner – before dinner

Se détendre is a reflexive verb meaning “to relax oneself,” i.e., “to relax” (intransitive, about a person).

• se détendre – to relax (oneself), to unwind
• détendre alone is transitive: to loosen/relax something (a muscle, a string, an atmosphere, etc.)

So:

• Ils vont au parc pour se détendre. – They go to the park to relax.
• Le massage détend les muscles. – The massage relaxes the muscles.

In your sentence, the city dwellers are relaxing themselves, so French needs the reflexive form se détendre.

After pour meaning “in order to / to (do something),” French uses the infinitive, not a conjugated verb:

• pour se détendre – in order to relax
• pour apprendre le français – to learn French
• pour trouver un emploi – in order to find a job

So pour ils se détendent is incorrect. You must say pour se détendre, with se détendre in the infinitive. The reflexive pronoun se is kept, but the verb isn’t conjugated.

Yes, that order is also correct:

• Beaucoup de citadins visitent cette galerie après le boulot pour se détendre.
• Beaucoup de citadins visitent cette galerie pour se détendre après le boulot.

Both are grammatical and natural. The difference is very slight:

• Original: puts a small focus on when they visit (after work), then gives the purpose (to relax).
• Reordered: slightly highlights the purpose (to relax), then mentions when (after work).

In everyday speech, both orders are acceptable and mean essentially the same thing.