Je montre le certificat d’immatriculation.

Because montre is the 1st person singular present tense form of montrer (to show).

• montrer = infinitive = to show
• je montre = I show / I am showing

This is a regular -er verb:

• je montre
• tu montres
• il / elle / on montre
• nous montrons
• vous montrez
• ils / elles montrent

So in this sentence, montre is the correctly conjugated verb for je.

It can mean both, depending on context.

French very often uses the simple present where English might use either:

• I show
• I am showing

So Je montre le certificat d’immatriculation could mean either:

• I show the registration certificate
• I am showing the registration certificate

French does have ways to stress an ongoing action, but the normal present tense is usually enough.

Because French usually requires an article before a noun.

Here:

• le certificat = the certificate

Also, certificat is masculine singular, so the definite article is le.

Compare:

• le certificat = the certificate
• un certificat = a certificate

So if you wanted to say I show a registration certificate, you would say:

• Je montre un certificat d’immatriculation.

Because d’ is a shortened form of de used before a vowel sound.

• de + immatriculation becomes d’immatriculation

This is called elision.

French does this often:

• de + école → d’école
• de + accord → d’accord
• de + immatriculation → d’immatriculation

So certificat d’immatriculation literally has the structure certificate of registration.

It is the direct object of the verb montre.

The structure is:

• Je = subject
• montre = verb
• le certificat d’immatriculation = direct object

In other words, it is the thing being shown.

This is why, if you replaced it with a pronoun, you would use le:

• Je le montre. = I show it.

No. Standard French does not contract je before a consonant.

You can only shorten je to j’ before a vowel or silent h:

• j’aime
• j’habite
• j’imagine

But here the next word is montre, which begins with m, a consonant, so it must stay:

• Je montre

Not:

• J’montre in standard written French

In very casual spoken French, people may reduce sounds, but the correct written form is Je montre.

montre is pronounced roughly like montr in one syllable, with a nasal vowel at the start.

A simple English-friendly approximation is:

• mohntr

A few useful points:

• the on is nasal, so it is not a full English on
• the final e is not pronounced
• the tr is pronounced together at the end

Also, this verb form montre sounds the same as the noun montre meaning watch.

So context tells you which one it is.

Yes. It is a standard expression, especially in administrative or driving-related contexts.

Literally, it is:

• certificat = certificate
• d’immatriculation = of registration

Together, it means the official registration certificate.

In real-life French, especially in France, you may also hear carte grise in everyday speech for a vehicle registration document, but certificat d’immatriculation is the formal term.

Because French often links nouns with de in a way that English may translate in several different ways.

Here:

• certificat d’immatriculation

Literally follows the pattern:

• certificate of registration

French does not say:

• certificat de l’immatriculation

because that would mean something more like certificate of the registration, referring to a specific registration event in a less natural way.

So de + noun is the normal structure here.

You would say:

• Je montre le certificat d’immatriculation au policier.
• or Je montre le certificat d’immatriculation à l’agent.

Here, le certificat d’immatriculation is still the direct object, and to the police officer is introduced by à.

So the pattern is:

• montrer quelque chose à quelqu’un
• to show something to someone

Examples:

• Je montre le document au policier.
• Je montre mes papiers à l’agent.

It is neutral and perfectly standard French.

• Je is standard
• montre is a normal everyday verb
• certificat d’immatriculation is a more official or administrative noun phrase

So the whole sentence sounds natural in a serious, practical context, such as dealing with documents, traffic control, or administration.

It is not slangy, and it is not unusually formal in grammar—just somewhat official in vocabulary because of the document name.