Oh having rewatched Félix recently, I can say that Émilie is very definitely dead, even without Astruc's tweet that confirmed it. The show never uses the term directly, most probably because it's children's television, but the words chosen all spell it out; the more ambiguous ones are even basically clarified.
I jotted down most of the references to what happened to Émilie mentioned in Félix, and here goes:
When Gabriel comes to talk to Adrien:
Gabriel: tant qu'elle est présente dans nos coeurs, elle est vivante. (As long as she's in our hearts, she's alive)
This is a very typical sentence people use when someone has died, to reassure the begrieved that the person isn't gone forever and that they're still around (it's of course more literal here since Émilie, although most probably actually dead id very well "conserved" so she can just "wake up" with the wish, and not just in a magical coma). Some people could argue that it could apply to someone who's missing as well, so let's continue with Adrien justifying his dad's anger to Plagg:
Adrien: Aujourd'hui ça fait un an que Maman est partie pour toujours (today marks one year since Mum left forever).
Here, we have another classic death litotes or understatement, as "partie pour toujours" is also used very often and would be understood in French as something unambiguous about her fate. There are less ambiguous formulations in the episode though, so let's continue.
I'm not going to dwell on the staging of Amélie's entrance, even though the bright light makes it look like a ghost apparition, but I will stop a bit on her comment about the Graham de Vanily's rings - she coos at the fact that Gabriel is still wearing his, and then says:
Amélie: Et celle d'Emilie tu l'as toujours j'imagine? (And Émilie's [ring], I suppose you still have it?)
I find it very hard to believe that if Émilie had just left, she'd have left her ring with Gabriel. If Amélie assumes (rightly) that he still has it, it's more plausible that it's because Émilie is dead, and he would have gotten it back before the funeral. Just a little something worth noting, but let's get back to more direct mentions:
Marinette: Qu'est-ce que tu dirais à un kwami qui a perdu sa maman? (What would you say to a kwami who'd lost his mother?)
I think we could stop there because that's probably explicit enough, "lose someone" is a phrase that translates fairly well, but there's more!
Adrien: Désolé de ne pas être venu à l'enterrement de ton père. (Sorry I didn't go to your father's funeral)
Adrien: Félix vient tout juste de perdre son père! Il est sans doute un peu perturbé! (Félix just lost his father! He's probably a little troubled!)
Plagg: Je suis désolé, mais ça n'est pas une raison! Toi tu ne touches pas à mon fromage, et pourtant tu as perdu ta mère, non? (I'm sorry, but that's no excuse! You don't touch my cheese, and yet you lost your mother, no?)
There. If it wasn't already clear, I think that really does it. The same expression "Lost", is used for both Felix's dad and Emilie, and we have an explicit mention of a funeral in the former's case, meaning that Émilie is also dead in-universe, and isn't just "missing".
That term was used in Ephemeral, as @trainsinanime mentioned; the journalist asked:
Journalist : La 100ème collection de la marque Gabriel est dédiée à votre mère disparue il y a peu - comment avez-vous accueilli cette idée? (Gabriel brand's 100th collection is dedicated to your mother, who disappeared recently - how did you take the idea?)
But in French, "disparu" is another understatement for death, even if it's also obviously used when someone's actually missing. The question is a delicate one to ask, so the journalist definitely wouldn't ask about Adrien's "mother who died recently" in that context. And then Gabriel later says:
Gabriel: 100 semaines qu'elle nous a quitté. (100 weeks since she left us)
Which echoes Adrien's words in Félix.
TL;DR: Émilie is dead, everyone knows it in-universe, the language used just doesn't reflect that when literally translated (like bouton d'or and golden button/buttercup 😉).
So it's not that Adrien, Amélie and co. Don't care about Émilie and that Gabriel is the only one with the sensible reaction ; it's actually the other way round. Adrien knows his mother is dead, he's sad about it and misses her a lot, but he's dealing with it in a mature way, acknowledging the fact that he'll never see her again. Gabriel's the one in denial, and who's completely over the top.
