The neocons like Kristol were never true conservatives/Republicans. They were an opportunistic parasitical political cult. They took advantage of the fact the conservatives love the military and they kept flying the security flag to trick us into overseas military adventures.
This became apparent after the Cold War removed the USSR as the main threat. During that time the neocon views lined up with the anti-communist views of the Reagan era. When the Cold War ended the neocon's parasitic nature and their parasitic agenda became more clear.
Neocons like Bill Kristol are not only not "true conservatives," they are as you point out by implication, not Conservative at all. My analysis of the phenomenon, during the Bush II Administration, was based entirely on the writing of their acknowledged "Godfather," Bill Kristol's father, who openly proclaims his ideological roots as a devotee of Leon Trotsky, the head of the Bolshevik Red Army, and thus the leading butcher in the Bolshevik Revolution.
The fact that the Washington Post chooses to treat Kristol as a "Conservative" leader, confirms his status with the Leftist media. It should be a red flag to any duped Conservative.
I have no idea who David French is; but if he is working with Kristol, he is not likely an American Conservative.
See Neocon Phenomenon, to understand how truly far from Conservative--or any shared values--are the Kristols.