Après le cours, la professeure note les contrôles dans son bureau.

In French, you usually need an article where English often does not. So English says after class, but French says après le cours.

Here, le cours most naturally means the class/the lesson that has just taken place. French prefers the article in this kind of expression.

They are related, but not the same.

• un cours = a lesson, class session, or course
• une classe = a classroom, or the group of students

In this sentence, après le cours means after the lesson/class session, so cours is the right word.

La professeure is a feminine form meaning the female teacher/professor.

A few notes:

• professeure is a common feminine form in modern French
• In everyday speech, many people simply say la prof
• Depending on region or style, you may also see other usage such as le professeur used generically, but la professeure clearly marks that the teacher is female

Often, not much — and sometimes not at all.

In many varieties of French, professeure is pronounced the same as professeur, especially in ordinary speech. The feminine difference is very clear in writing, but not always strongly different in pronunciation.

So a learner should not be surprised if the spoken form sounds like professeur even when the written word is professeure.

Note is the 3rd person singular present of noter.

So:

• je note
• tu notes
• il/elle note

With la professeure, the form is note because the subject is she.

In this sentence, noter most likely means to grade/mark or to record marks for the tests, depending on context.

No — this is a classic false friend.

In a school context, un contrôle usually means:

• a test
• a quiz
• sometimes an assessment

So les contrôles here means the tests or the test papers, not controls in the English sense.

Les contrôles suggests specific tests — the ones already known from the situation, probably the tests from that class.

French often uses the definite article where English might be more flexible.

• les contrôles = the tests / those tests
• des contrôles = some tests

In this sentence, les contrôles sounds natural because the tests are understood from the context.

Yes, but the meaning shifts slightly.

• corriger les contrôles = to correct/mark the tests, checking answers
• noter les contrôles = to grade the tests, assign marks, or record grades

A teacher often does both, but the focus is different:

• corriger focuses on checking and correcting
• noter focuses on the grade or mark

Because French possessive adjectives agree with the thing possessed, not with the owner.

Here, bureau is a masculine singular noun, so you use son:

• son bureau = her office / his office

It does not matter that the owner is female.

Compare:

• son bureau because bureau is masculine
• sa salle because salle is feminine

Dans son bureau means in her office — literally, inside that room.

You could also see à son bureau, but that often means at her desk or at her office/workplace, depending on context.

So the difference is roughly:

• dans son bureau = in her office
• à son bureau = at her desk / at her office

Also, bureau itself can mean office or desk, depending on the sentence.

It is the present tense.

In French, the present tense can mean:

• something happening now
• a habitual action
• a general fact
• a narrative action

So this sentence could mean:

• she is grading the tests now, after class
• or this is what she usually does after class

You need context to know which reading is intended.

Not always, but it is perfectly normal.

The comma separates the opening time phrase from the main clause:

• Après le cours, la professeure note les contrôles dans son bureau.

Without the comma, the sentence is still understandable:

• Après le cours la professeure note les contrôles dans son bureau.

In short sentences, French punctuation can be a little flexible here, but the comma makes the structure clearer.