La neuvième leçon commence.

Because leçon is a feminine singular noun. In French, the definite article has to match the noun’s gender and number:

• le = masculine singular
• la = feminine singular
• les = plural

So you say la leçon.

Neuvième is the ordinal adjective meaning ninth.

It comes from neuf (nine), but it does not become neufième. Instead, French changes the f to v and adds -ième:

• neuf → neuvième

This is a normal irregular pattern for this number.

Yes. Ordinal adjectives agree with the noun they describe in gender and number.

In this sentence, neuvième describes leçon, so it agrees with it. For neuvième, the masculine and feminine singular forms are spelled the same, so you do not see a visible change here.

• masculine singular: neuvième
• feminine singular: neuvième
• plural: neuvièmes

So the agreement is there, even though the singular form looks identical.

In French, ordinal numbers such as premier, deuxième, troisième, neuvième, etc. normally come before the noun:

• la neuvième leçon
• le troisième chapitre
• la première page

So this word order is the standard one.

Commence is the present indicative form of commencer.

Here it is the third-person singular form, because the subject is la neuvième leçon, which is singular.

Conjugation of commencer in the present:

• je commence
• tu commences
• il/elle/on commence
• nous commençons
• vous commencez
• ils/elles commencent

So in this sentence, commence matches the singular subject.

Because the subject is singular: la neuvième leçon.

The main noun in the subject is leçon, which is singular. Neuvième is just describing that noun; it does not make the subject plural.

So the verb must also be singular:

• La neuvième leçon commence.

If the subject were plural, the verb would change:

• Les neuvièmes leçons commencent.

Yes. The French present tense often covers both meanings that English separates into:

• begins
• is beginning

So La neuvième leçon commence can naturally correspond to either, depending on context.

This is very common in French: the present tense is often broader than in English.

Commencer is the infinitive form, meaning to begin or to start.

Commence is a conjugated form of that verb, used with a subject:

• commencer = to begin
• la leçon commence = the lesson begins

French sentences normally need a conjugated verb, not an infinitive by itself, unless you are using a special construction.

The mark under the c in leçon is called a cedilla: ç.

Its job is to make the c sound like s before a, o, or u.

So:

• ça sounds like sa
• leçon has an s sound in the middle

Without the cedilla, lecon would suggest a hard k sound before o, which would be wrong.

A careful pronunciation is approximately:

la nœ-vyèm luh-son ko-mons

More closely in IPA: /la nø.vjɛm lə.sɔ̃ kɔ.mɑ̃s/

A few useful points:

• neuvième has one syllable that sounds roughly like vyèm
• leçon ends with a nasal sound; the final n is not pronounced as a separate n
• commence ends with a soft s sound because c before e is soft

There is no special liaison to worry about in this sentence.