The difference
Gin, lemon and syrup in both. The French 75 is topped with Champagne; the Earl Grey MarTEAni infuses its gin with Earl Grey tea and adds egg white for a silky foam, and is the sweeter of the two.
By the numbers
The Earl Grey MarTEAni uses egg white where the French 75 uses sparkling wine; both have lemon juice, simple syrup and gin. In parts, an Earl Grey MarTEAni is 1 lemon, 1¼ syrup and 2 gin; a French 75 is 2 gin, 1 lemon, 1 syrup and 4 bubbles. By volume, the Earl Grey MarTEAni is 46% spirit, 31% syrup and sugar and 23% citrus; the French 75 is 50% mixer and juice, 25% spirit, 13% syrup and sugar and 12% citrus.
The French 75 is the stronger drink in the glass (12.5% ABV against 9.6%), but being smaller it holds about the same alcohol (1.01 and 1.08 standard drinks). The Earl Grey MarTEAni has more calories (about 192 against 150) and more sugar (19.2 g against 10.3 g). Both are shaken; the Earl Grey MarTEAni is served in a martini glass, the French 75 in a flute.