Begs the question...

They would be using the starter beam weapons. We don't have the means to change what fighters use right now.

I did make a post on carriers, showing the results of my tests. Other people have posted their results as well.
https://forums.galciv3.com/460722/page/1/#3518704

It is 'hardcoded' in the xml files.

From ShipComponentDefs.xml:

<ShipComponent>
<InternalName>AssaultCarrierModule</InternalName>
...
<Type>AssaultCarrierModule</Type>
...
</ShipComponent>

From ComponentClassDefs.xml:

<ComponentClass>
<UniqueID>AssaultCarrierModule</UniqueID>
<PrimaryStat>AssaultFighters</PrimaryStat>
</ComponentClass>

<ComponentClass>
<UniqueID>EscortCarrierModule</UniqueID>
<PrimaryStat>EscortFighters</PrimaryStat>
</ComponentClass>

From FactionDefs.xml:

<Faction>
<InternalName>FACTION_TERRAN</InternalName>
...
<InitialAssaultFighter>TerranSniper</InitialAssaultFighter>
<InitialEscortFighter>TerranGuardian</InitialEscortFighter>
<InitialGuardianFighter>TerranKnight</InitialGuardianFighter>
...
</Faction>

There is a definition for an "EscortCarrierModule" class which will use Escort Fighters (the Guardian). But there is no ship component of this class, as of yet. However it presence and the definitions of InitialEscortFighter and InitialGuardianFighter might indicate that other CarrierModule component(s) are to follow.

Funny thing:

The initial Escort Fighter is the Guardian, while the Initial Guardian Fighter is the Knight . Confused? You won't be, after this week's episode of... 

Personally I think Fighters should have Guns on them rather than lasers. That would force them to close the distance to target and be actually more realistic at least for my thoughts one that a single man load-out would be.