Je n’aime pas marcher sur la moquette avec des chaussures mouillées.

Because French usually contracts ne before a vowel sound.

So:

• ne aime → n’aime

This is called elision. You see it a lot:

• je n’aime pas
• je n’ai pas
• je n’écoute pas

It happens because aime starts with a vowel.

In standard French, negation usually goes around the conjugated verb.

Here, the conjugated verb is aime:

• Je n’aime pas

So the structure is:

• Je = I
• n’... pas = not
• aime = like / love

Then the rest of the sentence follows:

• marcher sur la moquette avec des chaussures mouillées

A useful thing to remember: in everyday spoken French, people often drop ne, so you may hear:

• J’aime pas marcher sur la moquette...

But in careful written French, ne ... pas is the standard form.

Because after aimer, French commonly uses the infinitive to talk about liking or not liking an action.

So:

• aimer + infinitive

Examples:

• J’aime lire. = I like reading / I like to read.
• Elle aime cuisiner. = She likes cooking / likes to cook.
• Je n’aime pas marcher... = I don’t like walking...

English can use either -ing or to + verb, but French normally uses the infinitive here.

Sur means on or onto, and it is the natural preposition for being or walking on a surface.

So:

• marcher sur la moquette = to walk on the carpet

French uses sur just as English uses on for many surfaces:

• sur le sol = on the floor
• sur la table = on the table
• sur le lit = on the bed

So sur is the expected choice here.

This is a very common vocabulary question.

• la moquette usually means carpet fitted to the floor, wall-to-wall carpet
• le tapis usually means a rug or smaller carpet you can lay down and move

So if you are talking about the carpet covering the floor of a room, moquette is often the better word.

Examples:

• Il y a de la moquette dans la chambre. = There is carpet in the bedroom.
• Il y a un tapis sous la table. = There is a rug under the table.

This phrase means with wet shoes.

Breakdown:

• avec = with
• des chaussures = some shoes / shoes
• mouillées = wet

French often uses avec in this kind of sentence to describe what someone has on or is using while doing something.

So:

• marcher ... avec des chaussures mouillées = to walk ... wearing wet shoes / with wet shoes on

It sounds natural in French and clearly describes the condition of the shoes while walking.

Great question, because learners often know that negatives can change un / une / des into de.

For example:

• J’ai des chaussures. = I have some shoes.
• Je n’ai pas de chaussures. = I don’t have any shoes.

But that change usually happens when the article is tied directly to the object of the negated verb.

Here, des chaussures mouillées is part of the prepositional phrase:

• avec des chaussures mouillées

The negation is on aime:

• Je n’aime pas

So the phrase with avec stays as it is:

• avec des chaussures mouillées

That is why des does not change to de here.

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

The noun here is chaussures:

• chaussure is feminine
• chaussures is plural

So the adjective mouillé must match:

• masculine singular: mouillé
• feminine singular: mouillée
• masculine plural: mouillés
• feminine plural: mouillées

Since chaussures is feminine plural, the correct form is:

• des chaussures mouillées

It describes the shoes.

In the phrase:

• avec des chaussures mouillées

the adjective mouillées comes right after chaussures, so it naturally modifies that noun.

So the idea is:

• the shoes are wet

Not:

• the carpet is wet

If you wanted to say the carpet was wet, you would attach the adjective to moquette, for example:

• la moquette mouillée = the wet carpet

Yes, you could, but the nuance is a little different.

• mouillé(e)(s) = wet
• humide(s) = damp / humid / slightly moist

So:

• des chaussures mouillées suggests the shoes are clearly wet
• des chaussures humides suggests they are damp rather than soaked

In this sentence, mouillées is the more natural choice if the idea is that the shoes are wet enough to make walking on carpet unpleasant.

Because marcher is a verb in the infinitive, not a noun.

In French, after aimer, you normally put the verb directly:

• aimer marcher
• aimer lire
• aimer nager

You do not need anything like le or de before the infinitive here.

So:

• Je n’aime pas marcher... = correct

In everyday spoken French, many speakers would drop ne and say:

• J’aime pas marcher sur la moquette avec des chaussures mouillées.

That is very common in conversation.

In more careful or formal French, especially in writing, you keep the full form:

• Je n’aime pas marcher sur la moquette avec des chaussures mouillées.

So both are useful to recognize:

• written / formal: Je n’aime pas...
• spoken / informal: J’aime pas...