Cette jupe va avec ce gilet.

Because jupe is a feminine singular noun, while gilet is a masculine singular noun.

French demonstrative adjectives change to match the gender and number of the noun:

• ce = this/that for masculine singular
• cet = this/that for masculine singular before a vowel sound
• cette = this/that for feminine singular
• ces = these/those for plural

So:

• cette jupe = this skirt
• ce gilet = this cardigan / vest

In French, every noun has a grammatical gender, and you usually have to learn it with the noun.

Here:

• la jupe = the skirt → feminine
• le gilet = the cardigan / vest → masculine

A good habit is to learn nouns with their article:

• une jupe
• un gilet

That way, you remember the gender more easily.

Because the subject is Cette jupe, which is singular.

The verb is aller, and here it is conjugated in the third person singular:

• je vais
• tu vas
• il/elle/on va
• nous allons
• vous allez
• ils/elles vont

Since cette jupe = it / this skirt, French uses va:

• Cette jupe va avec ce gilet.

If the subject were plural, you would use vont:

• Ces jupes vont avec ce gilet.

Yes. Literally, aller avec means to go with.

In clothing contexts, it means:

• to match
• to go well with
• to suit together

So Cette jupe va avec ce gilet means the skirt and the cardigan look good together.

This is very similar to English This skirt goes with this cardigan.

No. It can be used more broadly for things that match or pair well together.

For example:

• Le rouge va avec le noir.
  Red goes with black.

• Ce vin va bien avec le poisson.
  This wine goes well with fish.

But it is especially common for:

• clothes
• colors
• styles
• food pairings

Yes. Some common alternatives are:

• s’accorder avec = to match / to coordinate with
• aller bien avec = to go well with
• bien se marier avec = to go well together, to pair nicely with

Examples:

• Cette jupe s’accorde avec ce gilet.
• Cette jupe va bien avec ce gilet.

Va avec is simple, common, and natural.

No, this is normal. In French, ce / cette / cet / ces already mean this or that, so you do not also use le / la / les.

So:

• ce gilet = this cardigan
• not le ce gilet

Likewise:

• cette jupe = this skirt
• not la cette jupe

French uses either:

• an article: la jupe, le gilet
• or a demonstrative adjective: cette jupe, ce gilet

Both are used with masculine singular nouns, but:

• ce is used before most consonant sounds
• cet is used before a vowel sound or a silent h

Examples:

• ce gilet = this cardigan
• cet homme = this man
• cet arbre = this tree

Since gilet begins with a hard g sound, French uses ce, not cet.

A simple pronunciation guide is:

Set zhüp va ah-vek suh zhee-lay

A few notes:

• cette sounds like set
• jupe has the French u sound, which is different from English
• va sounds like vah
• avec is usually pronounced ah-vek
• gilet sounds like zhee-lay

Also, in natural speech, French rhythm matters a lot, so it helps to listen and repeat the whole sentence as one unit.

Yes. In many cases, ce, cet, cette, and ces can mean either this or that, depending on context.

So:

• cette jupe can mean this skirt or that skirt
• ce gilet can mean this cardigan or that cardigan

If French speakers want to stress this one or that one, they can use:

• ce ...-ci = this ...
• ce ...-là = that ...

For example:

• Cette jupe-ci va avec ce gilet-là.
  This skirt goes with that cardigan.

Because avec is a preposition meaning with, and it follows the verb phrase va in the expression aller avec.

The structure is:

• subject + aller + avec + noun

So:

• Cette jupe = subject
• va = verb
• avec ce gilet = with this cardigan

This is the normal French word order here.

Yes, it sounds natural and correct.

A French speaker might also say:

• Cette jupe va bien avec ce gilet.
• Cette jupe s’accorde bien avec ce gilet.

Adding bien makes it sound a little more clearly like matches well. But Cette jupe va avec ce gilet is already perfectly natural.