En la cartelera de esta semana hay una comedia francesa y un drama español muy famosos.

Here cartelera does not mean a literal billboard. In Spain, la cartelera often means the listings / what’s on / the programme, especially for films, theatres, or shows.

So En la cartelera de esta semana means something like In this week’s listings or In the programme for this week.

Spanish uses en because the idea is that these films appear in the listings.

So:

• en la cartelera = in the listings / on the programme

This is the natural preposition here. English might say in this week’s listings or on this week’s programme, but Spanish uses en.

Because de esta semana is attached to cartelera and means of this week or for this week.

So:

• la cartelera de esta semana = this week’s listings

Spanish often uses de where English uses an apostrophe or a noun used like an adjective:

• el partido de hoy = today’s match
• la película de ayer = yesterday’s film
• la cartelera de esta semana = this week’s listings

Hay is used to say that something exists or is present somewhere: there is / there are.

So here, the sentence is introducing what is in the listings:

• hay una comedia... y un drama... = there is/are a comedy... and a drama...

Also, hay is invariable in standard Spanish: it does not change for singular or plural.

• hay una película
• hay dos películas

By contrast, está / están usually tells you where something specific is located:

• La película está en la cartelera = The film is in the listings

That is grammatical, but it is a different structure and less natural for introducing the items in the programme.

Because the nouns have different grammatical genders:

• comedia is feminine → una comedia
• drama is masculine → un drama

A very common learner trap is that drama ends in -a, but it is still masculine. Spanish has several masculine nouns of Greek origin that end in -a, for example:

• el drama
• el problema
• el tema
• el programa

So you have to learn the gender of the noun, not just rely on the ending.

Because adjectives in Spanish must agree with the noun they describe in gender and number.

• comedia is feminine singular → francesa
• drama is masculine singular → español

So:

• una comedia francesa
• un drama español

This is normal adjective agreement.

Because in Spanish, descriptive adjectives such as nationality adjectives usually come after the noun.

So Spanish naturally says:

• una comedia francesa
• un drama español

not usually:

• una francesa comedia
• un español drama

This is one of the most basic word-order differences from English.

In Spanish, nationality words and language names are usually written in lower case.

So Spanish writes:

• un drama español
• una actriz francesa
• hablo inglés
• estudio español

This is different from English, which capitalizes Spanish, French, English, etc.

Because muy famosos describes both items together: the comedy and the drama.

Since it refers to two nouns, the adjective must be plural:

• famosos

And when Spanish has a mixed group containing a masculine noun and a feminine noun, the default agreement is masculine plural:

• una comedia
  • un drama → famosos

So:

• una comedia francesa y un drama español muy famosos

means that the two works are very famous.

If only the drama were being described as famous, you would expect:

• un drama español muy famoso

If only the comedy were being described as famous, you would expect:

• una comedia francesa muy famosa

Because muy is used before adjectives and adverbs to mean very.

Here famosos is an adjective, so:

• muy famosos = very famous

Compare:

• muy famoso = very famous
• muchos famosos = many famous people / many celebrities

So:

• muy
  • adjective/adverb
• mucho/mucha/muchos/muchas
  • noun, or as another kind of modifier depending on the structure

Yes, very natural.

The structure is:

• En la cartelera de esta semana = setting/context
• hay = there is/are
• una comedia francesa y un drama español = the things being introduced
• muy famosos = final adjective phrase describing both

That is a normal and idiomatic Spanish sentence. English and Spanish organize information differently, but nothing here is unusual for standard Spanish.