I don't read French and I don't think much has been published about this question. However, I think we can safely say that Chiappe would have been expected to be strongly loyal to the Vichy regime, just as was his replacement Henri Dentz.
A book by Martin Thomas explains that Gabriel Puaux, Chiappe's predecessor, was in office before the Vichy government came to power and that his committment to their policies was open to question.
Though Gabriel Puaux brought the French Levant into line with Vichy
in July 1940, it was no secret that the High Commissioner had
previously worked well with the British in Palestine. [...] Unwilling to side with the British, Puaux was equally reluctant to act against them. [...] Puaux’s equivocal reaction to the abortive Free French coup in September 1940 indicated that the High Commissioner lacked enthusiasm for Vichy’s more aggressive self-defence against Britain and Free France.
This was likely on the mind of the Deputy Prime Minister, Pierre Laval, both when he appointed Jean Chiappe in the first place and again when he selected Dentz to replace him. At Chiappe's funeral, Laval directly told Dentz that he
had personally selected Chiappe for the Beirut post. This was a strong indication of the likely direction of French policy in the Levant. Dentz was assigned more sweeping powers than his predecessor. He not only took on the job of High Commissioner but became regional military commander as well. Though clearly not the creature of Laval that Jean Chiappe appears to have been, Dentz believed fervently in Pétain and the cause of Vichy’s National Revolution.
While I don't see much more detail about the relationship between Laval and Chiappe, Thomas clearly implies that they had one, and as the Wikipedia article linked to in the question also makes clear, Chiappe would have been known to many other far-right figures in France and perhaps beyond.