The difference, by the numbers
They have no ingredient in common: the Death Flip has tequila, Jägermeister, Yellow Chartreuse, simple syrup and whole egg, the French Connection Cognac and amaretto. In parts, a Death Flip is 2 tequila, 1 Jägermeister and 1 Chartreuse; a French Connection is 1 brandy and 1 amaretto. By volume, the Death Flip is 49% spirit and 49% liqueur; the French Connection is 50% spirit and 50% liqueur. Different bottles, similar balance: that makes them close cousins on the ratio map.
The French Connection is the stronger drink in the glass (27.2% ABV against 13.4%), but being smaller it holds about the same alcohol (1.34 standard drinks each). The Death Flip has more calories (about 231 against 173), but the French Connection has more sugar (10.5 g against 7.4 g). The Death Flip is shaken and served in a coupe; the French Connection is built and served in a rocks glass.