Metaphor ReFantazio pits you against Gideaux and several other pretenders to the throne. As a representative of the church, he will prove to be a tough consumer-especially as you cannot challenge him to his face. His status as a pretender to the throne grants him absolute protection from the King's Blessing; you are not quite so fortunate as of yet.
Similar to this RPG boss battle, in order to defeat this battle the correct Affinities must be equipped against Gideaux. Of course, the conflict was neither long nor hard but very important, setting the stage for all the later ones. This is as simple as dealing with Gideaux.
In Metaphor ReFantazio, the battle with Gideaux was a decision of when to intervene to assist or not. Tell them "yes." No matter how paranoid Glodell is, things will turn out best for you.
As it happens, ingratiating Louis is the main quest you've got going on at the moment, so it will do you some good. Glodell won't be particularly thankful that you're defending him, but it's the right thing to do to save him, as he's one of Louis's thugs.
In Metaphor ReFantazio, you are required to attack the two allies which Gideaux brought along with him in the fight rather than attacking him directly. You need to defeat the Mage first, and then he will be accompanied by a Spearmonk and a Mage Monk.
Trying to compete against these spells is just painful frustration. Physical attacks against the Mage Monk are the best option as most of the spells have no effect on him. One of the best followers you could have was Hulkenberg in the role of Brawler. I had to keep casting spells at the Mage Monk regardless of whether he was a Brawler, Healer, or Mage because my party relied heavily on magic. Thus, zeroing in on the Spearmonk would be appropriate.
It was quite a big help to have Strohl here as my Mage since this is weak to Ice Magic. Let me warn you, though: this boss fight is not a picnic. The Area of Effect strike by the Mage Monk is devastating if you are weak to ice. Also, watch out for its Wind Magic ability. Every now and then, Gideaux will attack and they can do so with either a single target or area-of-effect light-based attack.
A Spearmonk is not going to be a cakewalk, as its attack reduces defenses and inflicts a load of direct damage. Stock up on healing and revival items before in-game time 6/26 and, just in case, a couple of Ice items. You should also be prepared for Gideaux to use Mage Benevolence-an extremely powerful Area of Effect Heal.
As irksome as it is to gradually enfeeble his comrades, it is much more galling to watch them regain most of their strength. Keep killing off allies one at a time, and eventually you'll triumph. The fight will be over once he and his ally are defeated.
The reward will be in saying that you helped Glodell out. Say you want to "help," and a Louis-themed conversation will start up. You can say you are running for office, and you did so in order to help him. He will like that, to which you can further progress in the story.
In this sense, knowing How to defeat Gideaux in Metaphor ReFantazio, allows you to get rid of another opponent and continue progressing in this interesting game.