À l’université, ils font de la recherche dans un laboratoire moderne.

À l’université means at university / at the university in the sense of an institution.

• French usually uses à with places that are institutions:
  
  • à l’école – at school
  • à l’hôpital – at the hospital
  • à l’université – at the university

We say à l’université (not à la université) because of elision:

• The noun université is feminine, so the basic form would be à la université.
• But when la comes before a vowel sound, the a is dropped and replaced with an apostrophe: à l’université.

Dans l’université would sound more like inside the university building, emphasizing the physical interior, and is much less common in the general meaning “at university”.

The comma is optional but very common when you put a location or time expression at the beginning of a sentence for emphasis or clarity:

• À l’université, ils font de la recherche…

You can absolutely put the location at the end instead, with no comma in the middle:

• Ils font de la recherche dans un laboratoire moderne à l’université.
• Ils font de la recherche à l’université, dans un laboratoire moderne.

Word order is flexible with these prepositional phrases; the choice mainly affects rhythm and emphasis, not grammar.

Ils is the subject pronoun they for:

• a group of all males, or
• a mixed group (at least one male), or
• a group whose gender you don’t specify.

Elles is used only for a group of all females.

On in modern French often means we or people in general, and you could say:

• À l’université, on fait de la recherche dans un laboratoire moderne.
  This would be more like At university, people do research… / We do research…, less specific than ils.

Font is the third-person plural (ils/elles) of the verb faire (to do / to make):

• je fais
• tu fais
• il/elle/on fait
• ils/elles font

In French, faire de la recherche is the natural way to say to do research.

• You do not normally say rechercher for academic research.
• Rechercher is more to look for / to search for something specific:
  
  • Je recherche mes clés. – I’m looking for my keys.

So ils font de la recherche is the standard expression for they do research / they conduct research.

In French, la recherche is usually treated as a mass noun: an activity or field, not something you normally count.

So for the general idea of doing research as an activity, French prefers the singular with a partitive article:

• faire de la recherche – to do research (as an activity).

If you want to insist on multiple specific projects or studies, you can use the plural:

• Ils font plusieurs recherches sur le cancer. – They are doing several studies on cancer.
  But that’s more specific than the original sentence.

In French, the default position for most adjectives is after the noun:

• un laboratoire moderne – a modern laboratory
• un livre intéressant – an interesting book

Some common, usually short adjectives (often about Beauty, Age, Goodness, Size – the so‑called BAGS adjectives) come before the noun:

• un grand laboratoire – a big lab
• une belle université – a beautiful university

Moderne normally comes after, so un laboratoire moderne is the natural word order.

Laboratoire is masculine singular, so:

• article: un
• noun: laboratoire
• adjective: moderne (masculine singular form)

If it were plural, you would have:

• des laboratoires modernes – modern laboratories
  Here both the noun and the adjective add -s: laboratoires, modernes.

Since the sentence talks about one lab (un laboratoire), the adjective must also be singular: moderne (no s).

• everyday conversation,
• a school textbook,
• a simple academic description.