Why is the subjunctive used here?
This is an extension of the subjunctive requirement when we're expressing wishes or desires. It requires the subjunctive form of pouvoir and a noun or an inversion with the appropriate pronoun. Here are other examples:
- Puissent les enfants être toujours heureux. = May the children always be happy.
- Puisse-t-il vous entendre. = Let us hope he can hear you.
- Puisse-je ne jamais revoir ça. = May I never see that again.
This is a complicated construction, and it's becoming more literary.
What are other ways this can be written in French?
To express wishes, you can of course use "souhaiter" or "esperer", but they're not as elegant as "pouvoir". (In this case, souhaiter requires the subjunctive, while esperer does not. It just so happens the subjunctive trouvent looks the same as the indicative trouvent.)
- Je souhaite qu'ils trouvent la paix. = I wish they find peace.
- J'espère qu'ils trouvent la paix. = I hope they find peace.
You may also use "que" + subject + subjunctive. This does not require pouvoir as a semi-auxiliary.
- Qu'ils trouvent la paix. = May they find peace.
In many cases, it all depends on the actual well-known expressions. For example the most common way to say "may he rest in peace" is "qu'il repose en paix."
As a bonus, I'm sure you know what this means in English:
- Que la Force soit avec toi.
No, the pouvoir is not necessary when using "que" in the beginning. They "may" meaning is already included in the "que". It's almost like repeating the meaning of "may" or "to be able to". Instead of "may they find peace, it sounds like "may they be able to find peace", which is redundant.