Le cordonnier pense que la semelle de ma chaussure peut encore tenir un mois.

Cordonnier means cobbler or shoemaker, but in modern everyday use it often refers specifically to someone who repairs shoes.

So in this sentence, le cordonnier is the shoe-repair person giving an opinion about the shoe.

French usually expresses possession with de:

• la semelle de ma chaussure = the sole of my shoe
• la couleur de la voiture = the color of the car

English often prefers ’s or a noun used like an adjective, but French generally uses de for this kind of relationship.

Because the sentence is talking about one shoe and specifically the sole of that one shoe.

• la semelle de ma chaussure = the sole of my shoe
• les semelles de mes chaussures = the soles of my shoes

If both shoes were being discussed, French would normally use the plural.

The subject is la semelle.

So the structure is:

• Le cordonnier pense que... = The cobbler thinks that...
• la semelle de ma chaussure = the sole of my shoe
• peut encore tenir un mois = can still last a month

It is the sole that can last another month, not the cobbler.

It often does mean to hold, but in this context tenir means something like:

• to hold up
• to last
• to stay usable
• to keep going

So la semelle peut encore tenir un mois means the sole can probably last or hold up for another month.

This is a very common extension of tenir for objects:

• Ces chaussures tiennent bien. = These shoes hold up well.
• La batterie tient encore deux heures. = The battery still lasts two hours.

Here encore means still or another.

So peut encore tenir un mois suggests:

• it is worn, but
• it can still last
• for another month

That idea of continuation is what encore adds.

Because with a conjugated verb plus an infinitive, French adverbs often go between them:

• peut encore tenir

This is very natural French word order.

You may also see slightly different placements in other sentences, but here peut encore tenir is the normal and smooth way to say can still last.

After verbs that already express duration or survival, French often uses a bare time expression:

• tenir un mois
• durer deux heures
• attendre dix minutes

So tenir un mois naturally means to last for a month.

You can sometimes use pendant in French, but here it is unnecessary and less natural.

Because penser que in an affirmative statement normally takes the indicative, not the subjunctive.

So:

• Le cordonnier pense que la semelle peut... is normal.

French usually uses the subjunctive after penser que only in certain cases, especially when the idea is doubtful, negative, or questioned:

• Je ne pense pas qu’il puisse venir.
• Penses-tu qu’il puisse venir ?

But in a straightforward statement of opinion, pense que ... peut is the expected pattern.

Peut is the present tense of pouvoir. Here it does not mean only present time; it expresses a current judgment about possibility.

So the cobbler is saying, right now, that the sole can probably last another month.

If you said pourra, that would be the future tense and would sound more like a prediction framed explicitly in the future. In this sentence, French naturally uses the present:

• peut encore tenir un mois = can still last another month

Yes, tenir encore un mois is also possible, and it means roughly the same thing.

Compare:

• peut encore tenir un mois
• peut tenir encore un mois

Both are understandable, but peut encore tenir un mois is very natural because encore closely modifies the idea of lasting.

So for a learner, the original word order is a very good model to remember.