J’attache sa médaille au collier pour qu’on puisse m’appeler si la chienne se perd.

Because je becomes j’ before a vowel sound. This is called elision.

• je attache → j’attache

The verb attacher means to attach or to fasten.
So J’attache means I attach or I’m attaching.

In everyday French, médaille can mean a tag worn by an animal, not just a medal in the English sense.

So in this sentence, sa médaille most naturally means her tag or her ID tag.

• sa = his/her/its
• médaille = medal, but here more naturally tag

French uses the same possessive adjective whether the owner is male or female. Sa agrees with the gender of médaille, which is feminine, not with the animal who owns it.

Because médaille is a feminine noun.

In French, possessive adjectives agree with the thing possessed, not with the possessor:

• son collier because collier is masculine
• sa médaille because médaille is feminine

So sa médaille does not tell you whether the owner is male or female. It only tells you that médaille is feminine.

Au is the contraction of à + le.

• à le collier → au collier

So attacher quelque chose au collier means to attach something to the collar.

This is a very common contraction in French:

• à + le → au
• à + les → aux

Use pour when it is followed by an infinitive and the subject stays the same.
Use pour que when a new clause follows with its own subject.

Here:

• J’attache... = subject: I
• qu’on puisse m’appeler = subject: on = someone/people

Because the second part has a different subject, French uses pour que.

Compare:

• Je ferme la porte pour dormir. = I close the door in order to sleep.
• Je laisse mon numéro pour qu’on puisse m’appeler. = I leave my number so that people can call me.

Because pour que is followed by the subjunctive in French.

The verb here is pouvoir, and the subjunctive form with on is puisse:

• qu’on puisse = so that people can / so that someone may be able to

So:

• on peut = indicative
• qu’on puisse = subjunctive

After expressions like pour que, the subjunctive is normally required.

On usually means one, people, someone, or we, depending on context.

In this sentence, qu’on puisse m’appeler means something like:

• so that someone can call me
• so that people can call me

It does not mean a specific person. It is an indefinite, general subject.

Because me becomes m’ before a vowel sound, just like je becomes j’.

• me appeler → m’appeler

Here m’ means me:

• appeler quelqu’un = to call someone
• m’appeler = to call me

So qu’on puisse m’appeler means so that someone can call me.

Because chienne specifically means a female dog.

• chien = dog / male dog
• chienne = female dog

So the sentence is specifically talking about a female dog. That is why later sa médaille can naturally refer to the female dog’s tag, even though sa itself is based on médaille, not on chienne.

It comes from the reflexive verb se perdre, which means to get lost.

• perdre = to lose
• se perdre = to get lost

So:

• si la chienne se perd = if the dog gets lost

This is different from perd by itself:

• elle perd son collier = she loses her collar
• elle se perd = she gets lost

Because French often uses the present tense after si for real or possible future situations.

So:

• si la chienne se perd literally looks like if the dog gets lost
• in natural English, it may be translated as if the dog gets lost or if the dog should get lost

This is normal French usage. French does not use a future tense after si in this kind of sentence.

Either can work, depending on context.

French present tense often covers both:

• I attach
• I am attaching

So J’attache sa médaille au collier could mean either:

• I attach her tag to the collar
• I’m attaching her tag to the collar

You need context to know which sounds best in English.

Grammatically, yes, sa could mean his, her, or its. French does not distinguish these forms here.

But in this sentence, the most natural interpretation is that the tag belongs to the female dog, because of the context:

• her tag
• the collar
• if the female dog gets lost

So while French grammar leaves it open, the meaning in context is clear.