Le copropriétaire donne une procuration à Paul.

In French, a singular countable noun usually needs an article or another determiner. So copropriétaire normally cannot stand alone in a basic sentence.

• le copropriétaire = the co-owner
• un copropriétaire = a co-owner

Here, le shows that we are talking about a specific co-owner, not just any co-owner.

Donne is the third-person singular present tense form of donner.

The subject is le copropriétaire, which is singular, so the verb must match it:

• je donne
• tu donnes
• il/elle/on donne
• nous donnons
• vous donnez
• ils/elles donnent

So Le copropriétaire donne... means The co-owner gives... or, depending on context, is giving.

It is the present indicative.

In English, the French present tense can correspond to several English forms depending on context:

• gives
• is giving
• sometimes even does give

So Le copropriétaire donne une procuration à Paul could be understood as:

• The co-owner gives a power of attorney to Paul
• The co-owner is giving a power of attorney to Paul

French often uses the simple present where English might prefer the progressive.

Like copropriétaire, procuration is a singular countable noun, so it normally needs an article.

• une procuration = a power of attorney / a proxy authorization
• la procuration = the power of attorney

Here, une means it is not being presented as a specific already-known document, just a procuration.

Also, procuration is a feminine noun, which is why the article is une, not un.

À Paul marks the recipient of what is being given.

With donner, French often works like this:

• someone donne quelque chose à quelqu’un
• someone gives something to someone

So in this sentence:

• le copropriétaire = the person doing the action
• une procuration = the thing being given
• à Paul = the person receiving it

That makes Paul an indirect object in French.

French contracts à + le into au and à + les into aux, but it does not contract à before a person’s name.

So:

• à le bureau → au bureau
• à les enfants → aux enfants
• à Paul stays à Paul

Since Paul is a proper name, no contraction happens.

Yes, that word order is also possible.

Both of these are grammatical:

• Le copropriétaire donne une procuration à Paul.
• Le copropriétaire donne à Paul une procuration.

The first version is often a more neutral way to present the thing first, then the recipient.
The second can put a bit more focus on Paul as the recipient.

French word order is somewhat flexible here, though the first version may feel more standard in many contexts.

Paul is the indirect object.

A useful way to see this is:

• What is given? → une procuration
  This is the direct object.
• To whom is it given? → à Paul
  This is the indirect object.

So with donner, the pattern is:

• donner quelque chose à quelqu’un
• to give something to someone

French expresses that idea differently. Instead of changing the verb, it uses à before the recipient:

• donner une procuration à Paul
• literally: give a power of attorney to Paul

So the English to Paul is simply represented by à Paul in French.

It is a noun meaning co-owner.

It is built from:

• co- = co-
• propriétaire = owner

So copropriétaire literally means co-owner.

In this sentence, it is the subject of the verb donne.

You can tell in this sentence because it uses une, the feminine singular indefinite article.

• un = masculine singular
• une = feminine singular

So:

• une procuration tells you that procuration is feminine.

As with many French nouns, grammatical gender has to be learned along with the word.

Yes. Donner is used not only for concrete objects but also for abstract things, documents, rights, permissions, and similar ideas.

For example, French can say things like:

• donner une autorisation = give/grant an authorization
• donner un conseil = give advice
• donner une procuration = give/grant a power of attorney

So this use of donner is completely natural.

A careful approximate pronunciation is:

Le copropriétaire donne une procuration à Paul
luh koh-proh-pree-eh-TAIR donn ewn proh-ky-ra-syon ah Pol

A few useful notes:

• le is usually pronounced luh
• donne sounds like donn
• une can be tricky for English speakers; its vowel does not exist exactly in English
• Paul sounds like Pol

Also, in normal speech, French rhythm matters a lot more than pronouncing every letter separately.