Je crois que la semelle de ma chaussure commence à se décoller.

Je crois que means I think / I believe that.

It is a very common way to soften a statement when you are not 100% sure. In this sentence, the speaker is not making a hard, definite claim; they are saying it seems to them that the sole is starting to come off.

Compared with je pense que, je crois que can sound a little more like I believe / I think, while je pense que is often closer to I think in everyday speech. In many situations, they are interchangeable.

French normally expresses this kind of possession with de:

• la semelle de ma chaussure = the sole of my shoe

This is the standard structure for body parts, parts of objects, and similar relationships:

• la porte de la voiture = the car door
• le toit de la maison = the roof of the house

English often prefers a compound noun like shoe sole, but French usually uses de.

It is singular because the speaker is talking about one shoe:

• ma chaussure = my shoe

If both shoes were involved, you would use the plural:

• les semelles de mes chaussures commencent à se décoller

French does use chaussure for a single shoe, even though English often talks about shoes as a pair.

La semelle is the sole of the shoe, the bottom part.

In this sentence, it most naturally means the outer sole or the part attached underneath the shoe, not the insole inside it. Since the sentence talks about it coming unstuck, the idea is that the sole is separating from the rest of the shoe.

The verb commencer is commonly followed by à + infinitive when it means to begin/start doing something:

• commencer à lire = to start reading
• commencer à tomber = to start falling
• commence à se décoller = is starting to come unstuck

So this is just the normal construction of the verb.

Because here the sole is not making something else come unstuck; it is itself coming unstuck.

That is why French uses the pronominal form se décoller.

Compare:

• décoller quelque chose = to unstick / peel off something
• se décoller = to come unstuck / peel away

So:

• La colle décolle l’étiquette would be wrong in meaning
• J’ai décollé l’étiquette = I peeled off the label
• L’étiquette se décolle = the label is coming off

Same idea with the sole.

Décoller without se is usually transitive: someone or something unsticks another thing.

• J’ai décollé le papier peint = I peeled off the wallpaper

Se décoller is intransitive/pronominal: the thing itself is becoming detached.

• Le papier peint se décolle = the wallpaper is peeling off

In your sentence, the sole is not actively doing the action to something else. It is separating from the shoe, so se décoller is the right form.

Because commencer is the conjugated verb, and se décoller stays in the infinitive.

French keeps the reflexive pronoun with the infinitive:

• Je vais me lever
• Il peut se tromper
• Elle commence à se décoller
  or here, with the subject la semelle: La semelle commence à se décoller

So the se belongs to décoller, not to commencer.

Because after an affirmative expression of belief like je crois que, French normally uses the indicative:

• Je crois qu’il vient
• Je crois que la semelle commence à se décoller

The subjunctive is more likely after negation or a question, because uncertainty is stronger:

• Je ne crois pas que la semelle commence / commence?
  In careful grammar, you often get the subjunctive here: Je ne crois pas que la semelle commence à se décoller

But in your sentence, the affirmative je crois que naturally takes the indicative.

Yes, but the meaning changes slightly.

• commence à se décoller = is starting to come unstuck
• est en train de se décoller = is in the process of coming unstuck

The original sentence focuses on the beginning of the problem.
The alternative focuses on the ongoing action.

So if you have just noticed the first signs, commence à se décoller is a very good choice.

Yes, it sounds natural and idiomatic.

It is a normal way to say that the sole of your shoe seems to be starting to come off. Depending on context, a native speaker might also say things like:

• Je crois que la semelle de ma chaussure se décolle.
• La semelle de ma chaussure est en train de se décoller.
• Je crois que ma semelle est en train de se décoller.

But your sentence is completely natural.

Sometimes yes, but it depends on context.

• la semelle de ma chaussure is clearer and more precise
• ma semelle may sound less natural if the context is not already obvious, because the sole is a part of the shoe, not usually something referred to independently

A French speaker might say ma semelle se décolle in casual speech if everyone already understands they mean the sole of their shoe. But your full version is safer and clearer for a learner.

Because ma is a possessive determiner, and in French you normally do not combine it with another article:

• ma chaussure = my shoe
• not la ma chaussure

French determiners like mon, ma, mes take the place of le, la, les.

If you wanted to talk about more than one sole or more than one shoe, several parts would change:

• Les semelles de mes chaussures commencent à se décoller.

Changes:

• la semelle → les semelles
• ma chaussure → mes chaussures
• commence → commencent

That is standard subject-verb agreement in French.

It has other meanings too.

A very common meaning of décoller is to take off for planes:

• L’avion décolle = the plane is taking off

It can also mean to unstick / remove by peeling depending on context.

So décoller has a basic idea of coming away from a surface / lifting off, and the exact meaning depends on what the subject is.

In your sentence, because the subject is la semelle, the meaning is clearly come unstuck / peel away.