Conjugation patterns
Verbs in -guer/-quer

Verbs in -guer and -quer

Verbs in -guer and -quer are regular. This means that they keep the u of their stem in all conjugations even when it is not necessary for the sound: je fatigue and c'est fatiguant.

Verb attaquer (to attack) at present

Verb fatiguer (to tire) at present

Arguer

A small exception, if you want to use the verb "arguer" (to argue). Indeed, one must always pronounce the u. In the conjugation of the verb arguer, there is a variant of conjugation with an umlaut: j'arguë, tu arguës, ils arguënt, ... This form is recommended by some dictionaries of French difficulty (Girodet, Collin...).

MBut that's not all, in the 1990 reform, the Académie française now recommends putting the umlaut on the u: j'argüe, tu argües, il argüe etc.

It is in front of this lack of consensus (or willingness to complicate things?) that The Conjugator has chosen to follow the Bescherelle and classifies this verb among the regular verbs.