Le cours de français est intéressant.

Because cours is a masculine noun in French, so it takes the masculine singular article le.
French nouns have grammatical gender (masculine or feminine), and it’s often arbitrary from an English point of view. You simply need to learn le cours as a fixed pair.

There is no reliable rule that always tells you whether a noun is masculine or feminine. Some word endings give strong hints, but -ours / -ours is not a clear pattern.
The safest method is to always learn a noun with its article, for example: le cours, la table, le livre, la chaise, and memorize the gender together with the word.

• Un cours is a course or lesson as a subject or teaching unit. It refers to the content or the teaching itself:
  
  • Le cours de français est intéressant. → The French course/lesson is interesting.
• Une classe can mean the group of students or the classroom as a social unit:
  
  • La classe est bruyante. → The class (group of students) is noisy.

So in your sentence, you’re talking about the French course, so cours is the correct word.

In le cours de français, the structure is cours de + school subject / field of study.
Here, de is like saying of in English: “course of French” → French course.

You would use du (= de + le) when de is followed by a masculine noun with an article, for example:

• Je parle du professeur. → I’m talking about the teacher.

In cours de français, français is used as a bare noun (no article) describing the type of course, so it stays de, not du.

That would mean something different.

• Le cours de français = a course whose subject is French (you are learning the French language).
• Le cours en français = a course that is taught in French, but the subject could be something else (history in French, math in French, etc.).

So for a language course, you normally say le cours de français.

In French, names of languages and adjectives of nationality are written with a lowercase letter:

• le français, l’anglais, le japonais

They are only capitalized when they’re part of a proper name (e.g., l’Académie française) or at the beginning of a sentence.
So de français is correctly written with a lowercase f.

Here français is a noun meaning “(the) French (language).”
The structure is literally “course of French”, where français is the name of the language.

As an adjective, français can also mean “French” (relating to France/the French language), for example:

• un livre français → a French book (adjective)
• le français → French (the language, noun)

In your sentence it functions as a noun.

In French, most adjectives go after the noun, not before it:

• un livre intéressant → an interesting book
• un film amusant → a funny film

Some common adjectives (like beau, petit, grand, bon, mauvais) often go before the noun, but intéressant normally goes after.

Since here we use it with être, it comes after the verb:

• Le cours de français est intéressant. → The French course is interesting.

Yes, adjectives in French must agree in gender and number with the noun:

• Masculine singular: intéressant
  
  • Le cours est intéressant.
• Feminine singular: intéressante
  
  • La classe est intéressante.
• Masculine plural: intéressants
  
  • Les cours sont intéressants.
• Feminine plural: intéressantes
  
  • Les classes sont intéressantes.

In your sentence, cours is masculine singular, so intéressant is masculine singular.

Cours is pronounced approximately like “koor” in English (with a short, tight French ou sound).

The final -s is silent in many French words in the singular form. In spelling, cours looks like a plural, but in practice:

• un cours (singular) and des cours (plural) are pronounced the same.
  You know whether it’s singular or plural from the article or context (un/le vs des/les).

Spoken naturally, you might hear:

• Le cours de français est intéressant.
  
  • cours de → usually no liaison: [kur də]
  • français est → liaison is possible: [frɑ̃.sɛ.z‿ɛ] (you may hear a z sound linking français and est)
  • est intéressant → often pronounced with a smooth link but no extra consonant: [ɛ.tɛ.ʁɛ.sɑ̃]

So the most noticeable possible liaison is between français and est.

Yes, but the meaning and focus change slightly:

• Le cours de français est intéressant.
  
  • Specifically describes the French course as interesting.
• C’est intéressant.
  
  • Means “That’s interesting” and is more general. It could refer to the course, or to something else that was just mentioned.

So C’est intéressant is correct French, but it’s less precise than naming le cours de français.

• Le cours de français est intéressant.

  • You’re talking about one specific course (for example, this semester’s French course).

• Les cours de français sont intéressants.

  • You’re talking about several courses or French courses in general, for example:
    
    • All the French courses at your school
    • All the French classes you’ve taken

The adjective changes to intéressants to agree with plural cours.

Le français est intéressant means “French (the language) is interesting.”
This talks about the language in general, not about a particular course.

• Le cours de français est intéressant. → The French course (one specific class) is interesting.
• Le français est intéressant. → French as a language is interesting.

They are both correct, but they don’t express exactly the same idea.