There are two different things that are combining here and causing your confusion. First, the fact that the verbs for "to listen" and "to hear" use two different words that are very similar, and second, the verb is conjugated in the potential form. Let's take a look to each point (1. and 2.) separately.
1. [聞く]{kiku} vs [聞こえる]{kikoeru}
Note that for some verbs related to interacting with the world through our senses (to look, to listen, etc.) there are several words to express the same action in Japanese depending on wether the action is intentional or not. This somewhat corresponds to the dichotomies listen/hear and look/see in English.
- [聞く]{kiku} → to purposely listen. For example,
[演奏]{ensou} [を]{wo} [聞く]{kiku} (I listen to a musical performance)
- [聞こえる]{kikoeru} → to unintendedly hear. For example,
[隣]{tonari} [の]{no} [部屋]{heya} [に]{ni} [ある]{aru} [テレビ]{terebi} [が]{ga} [聞こえる]{kikoeru} (I hear the television next door).
The same can be said of [見る]{miru} (to purposely look at) and [見える]{mieru} (to see, to be visible).
So even if [聞く]{kiku} and [聞こえる]{kikoeru} are related, it's better if you regard them as different words, as @Karl Knecthel pointed out. In your original sentence, the verb is [聞ける]{kikeru}, which ultimately comes from conjugating [聞く]{kiku} (and not [聞こえる]{kikoeru}) to the potential form.
2. Potential form of [聞く]{kiku}
To make the potential form of some types of verbs, the last hiragana ending in "u" is replaced by the hiragana with the same consonant but ending in "e" + "ru":
- [飲む]{nomu} To drink → [飲める]{nomeru} To be able to drink
- [聞く]{kiku} To listen → [聞ける]{kikeru} To be able to listen
Now, [聞く]{kiku} is a transitive verb so it takes を{wo} to mark objects, but when using the potential form of a verb, i.e. [聞ける]{kikeru}, the particle を{wo} changes to が{ga}. You can find plenty of posts here discussing this change, as @aguijonazo commented. You can also find instances where を{wo} is used instead of が{ga} to mark the object of a potential verb, but in general the rule is that potential verbs take が{ga}. Using the previous potential verbs as an example:
[ジュース]{juusu} [を]{wo} [飲む]{nomu} ( [I] drink juice)
[お酒]{osake} [が]{ga} [飲めない]{nomenai}。 ( [I] can't drink alcohol)
[ラジオ]{rajio}を[聞く]{kiku}。 ( [I] listen to the radio)
[日本]{nihon} [に]{ni} [いながら]{inagara}、[フランス語]{furansugo} [の]{no} [ラジオ]{rajio} [番組]{bangumi} [が]{ga} [聞ける]{kikeru}。 ( [You] can listen to radio programs in French while in Japan)
As @aguijonazo pointed out, you can also find instances where を{wo} is used instead of が{ga} to mark the object of a potential verb, but in general the rule is that potential verbs take が{ga}.
3. An example with [聞こえる]{kikoeru}
In order to highlight the difference between [聞ける]{kikeru} and [聞こえる]{kikoeru} in your context, let's think of an scenario involving the radio where it makes sense to use [聞こえる]{kikoeru} (to be heard, to hear) but not [聞ける]{kikeru} (to be able to listen to):
[ラジオ]{rajio} [で]{de} [ロック]{rokku} [の]{no} [番組]{bangumi} [を]{wo} [探していたら]{sagashiteitara}、[フランス語]{furansugo} [の]{no} [番組]{bangumi} [が]{ga} [聞こえてきた]{kikoetekita}。 While looking for a rock program in the radio, I could hear a French program.
As you can see, [聞こえる]{kikoeru} also takes the particle が{ga} but for different reasons than [聞ける]{kikeru}, i.e. because [聞こえる]{kikoeru} is an intransitive verb. Also note that even though I used "could" for the English translation of this last example sentence, this is not the potential form of [聞く]{kiku}, but the different verb [聞こえる]{kikoeru}.
