Je mets une housse propre sur le matelas.

Because the subject is je.

The verb here is mettre (to put / to place), and in the present tense it changes like this:

• je mets
• tu mets
• il / elle / on met
• nous mettons
• vous mettez
• ils / elles mettent

So Je mets means I put / I am putting.

A useful thing to notice: je mets and il met are pronounced the same in everyday speech, even though they are spelled differently.

It can mean both.

In French, the simple present often covers both ideas:

• I put
• I am putting

So Je mets une housse propre sur le matelas can mean either:

• I put a clean cover on the mattress
• I am putting a clean cover on the mattress

French usually does not need a separate am + -ing form the way English does. Context tells you which meaning is intended.

Une housse is a cover that goes over something.

Depending on context, it could be a cover for:

• a mattress
• a pillow
• a sofa
• a car seat
• a suitcase, etc.

In this sentence, because it says sur le matelas, une housse is a mattress cover.

Also notice that housse is feminine, which is why it uses une.

Because propre usually comes after the noun in French.

So:

• une housse propre = a clean cover

In English, adjectives usually come before the noun: a clean cover.
In French, many adjectives come after the noun, especially descriptive ones like propre (clean).

So this word order is normal:

• un matelas propre
• une chambre propre
• une housse propre

No. Propre has more than one common meaning.

It can mean:

• clean
• one's own

Examples:

• une housse propre = a clean cover
• ma propre chambre = my own room

In your sentence, propre clearly means clean.

Because sur means on / onto.

With mettre sur, French often expresses the idea of placing something onto a surface or over something:

• mettre un livre sur la table = to put a book on the table
• mettre une housse sur le matelas = to put a cover on the mattress

Even though a mattress cover goes around the mattress, French commonly uses sur here.

So sur le matelas is the natural expression.

French often uses the definite article (le, la, les) where English might use the, a, or even no article depending on context.

Here, le matelas refers to the specific mattress involved in the situation: the mattress you are covering.

So sur le matelas means:

• on the mattress

This sounds natural because both speaker and listener can identify which mattress is meant.

Matelas is masculine, so it takes:

• le matelas
• un matelas

There is no perfect way to guess every noun’s gender, so it is best to learn nouns together with their article:

• une housse
• le matelas

That is much more useful than memorizing the noun alone.

A simple pronunciation guide is:

zhuh may oo-n ooss propr syr luh ma-ta-lah

A few helpful notes:

• Je sounds like zhuh
• mets sounds like may
• housse sounds like ooss
• sur has the French u sound, which is hard for English speakers
• the final s in mets is silent
• the final s in matelas is also silent

In natural French, it flows together smoothly: Je mets une housse propre sur le matelas.

Yes. Mettre is an important and very common verb, but it is irregular.

A few useful things to remember:

1. In the present tense:

   • je mets
   • tu mets
   • il met

2. In nous and vous, the stem looks different:

   • nous mettons
   • vous mettez

3. It is used in many everyday expressions, not just for physically putting something somewhere.

Examples:

• mettre la table = to set the table
• mettre un pull = to put on a sweater
• mettre du temps = to take time

So this is a very worthwhile verb to learn well.

Yes.

That version means more specifically:

• I am in the middle of putting a clean cover on the mattress
• I am putting a clean cover on the mattress right now

Je mets... is the normal, simple way to say it.
Je suis en train de mettre... is more explicit and emphasizes that the action is happening right now.

So:

• Je mets une housse propre sur le matelas. = normal, everyday wording
• Je suis en train de mettre une housse propre sur le matelas. = stresses the ongoing action