I would have left Gaudu at home & then sent him to the Vuelta. If he can't podium another GT, he can't exactly demand full team support in the Tour.
And Gaudu is the issue here, not Pinot. There's no reason why all 3 riders (Gaudu, Pinot & Démare) can't coexist on the same team, i.e. the issue is Gaudu has been presented as a potential French Tour winner for years & some of his behavior over the past year (including his public outburst against Démare) certainly makes it appear like pressure might be getting to him.
Who knows, maybe Gaudu will do well in the TdF & disprove this post but IMO there's some very typically concerns signs that Gaudu is going to have some problems next month.
He seems to react badly when things don't go his way, like for example his immediate response after his bad result in the Dauphiné was to handwave any concern about his form & then have a go at "online haters" who abuse him. None of that was constructive, no matter how true (sadly, all the top riders get abused on social media).