Cette entreprise est internationale, et ses valeurs correspondent aux miennes.

Because entreprise is a feminine singular noun.

French demonstratives agree with the noun:

• ce = masculine singular
• cet = masculine singular before a vowel sound
• cette = feminine singular
• ces = plural

So:

• ce livre = this book
• cet hôtel = this hotel
• cette entreprise = this company
• ces entreprises = these companies

Here, entreprise means company or business.

Although it looks like the English word enterprise, in everyday French une entreprise is the normal word for a company. It is a feminine noun, which is why you get cette entreprise.

Because adjectives in French usually agree with the noun they describe.

Since entreprise is feminine singular, the adjective must also be feminine singular:

• masculine: international
• feminine: internationale

So:

• un groupe international
• une entreprise internationale

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

The owner here is cette entreprise, which is singular, so we need a form meaning its. But the possessed thing is valeurs, which is plural, so the correct form is ses.

Compare:

• sa valeur = its value
• ses valeurs = its values

So even though the company is singular, valeurs is plural, which is why French uses ses.

Because leurs is used when the owner is plural.

Here the owner is just one thing: cette entreprise. So French uses the singular-owner set:

• son / sa / ses = his, her, its

If there were several companies, you would use:

• leur / leurs = their

So:

• Cette entreprise et ses valeurs = this company and its values
• Ces entreprises et leurs valeurs = these companies and their values

Yes. In normal pronunciation, ses and ces sound the same: say.

You tell them apart by meaning and spelling:

• ses valeurs = his/her/its values
• ces valeurs = these/those values

This is a very common point of confusion for learners, because the pronunciation does not help you distinguish them.

Because the subject of the verb is ses valeurs, which is plural.

The verb is correspondre. In the present tense:

• je corresponds
• tu corresponds
• il/elle correspond
• nous correspondons
• vous correspondez
• ils/elles correspondent

Since valeurs is plural, French uses correspondent.

Also, the final -ent here is not pronounced.

Because correspondre normally takes the preposition à.

So French says:

• correspondre à quelque chose

In this sentence:

• ses valeurs correspondent aux miennes

This is different from English, where match can take a direct object:

• English: Its values match mine
• French: Ses valeurs correspondent aux miennes

So à is required by the verb.

Because aux is the contraction of à + les.

The underlying structure is:

• à les miennes → aux miennes

French always contracts à + les into aux.

You also see:

• au = à + le
• aux = à + les

So correspondent aux miennes literally follows the pattern correspond to mine.

Because mes is a possessive adjective, while les miennes is a possessive pronoun.

• mes must be followed by a noun: mes valeurs
• les miennes replaces the noun: mine / my ones

In this sentence, French avoids repeating valeurs, so it uses the pronoun:

• ses valeurs correspondent aux miennes

Also, miennes agrees with the noun it replaces, valeurs, which is feminine plural.

The full set is:

• le mien = mine (masculine singular)
• la mienne = mine (feminine singular)
• les miens = mine (masculine plural)
• les miennes = mine (feminine plural)

Yes, that is grammatically correct.

But French often prefers aux miennes to avoid repeating valeurs:

• ses valeurs correspondent à mes valeurs = correct, but repetitive
• ses valeurs correspondent aux miennes = more natural and elegant

So the sentence uses a possessive pronoun simply to sound smoother.

Not really. It is optional here.

You can write:

• Cette entreprise est internationale et ses valeurs correspondent aux miennes.

The comma adds a slight pause and can make the sentence feel a little more balanced, but it is not required. French generally uses commas before et less often than English does.