Learn French: Je doute qu'ils aient les compétences. - I doubt that they have the skills.

The phrase douter que (to doubt that) expresses uncertainty, which is a classic trigger for the subjunctive mood in French. Because you are expressing doubt about them having the skills, the following verb must be in the subjunctive.

What verb is aient, and how do I conjugate it in the subjunctive?

Aient is the subjunctive form of the verb avoir (to have) for the pronoun ils (they). Avoir has a highly irregular subjunctive stem, so its forms (aie, aies, ait, ayons, ayez, aient) just have to be memorized.

If I change this to the reflexive verb se douter (Je me doute que...), does it still use the subjunctive?

No, and the meaning completely changes! Se douter que means to suspect or guess that something is true. Because it expresses a strong belief rather than doubt, it takes the standard indicative mood instead of the subjunctive: Je me doute qu'ils ont les compétences (I suspect they have the skills).

Why use the definite article les in les compétences instead of des?

In this context, les compétences refers to the specific skills required for a particular task or job, rather than just 'some skills' in general. It matches the English translation 'the skills' perfectly.