The original recipe for the French 75 was built on a foundation of cognac, rather than the gin with which most are familiar. In the late 19th century, an outbreak of phylloxera throughout Europe destroyed much of the region's vineyards, which in turn depleted the available supply of cognac (which is distilled from wine). This cognac shortage encouraged bartenders to re-formulate the cocktail with gin, which was notably more accessible at the time.
Today it's possible to find this drink built with either spirit. A gin-based French 75 tends to be a bit dry and 'sharp', whereas cognac - which has a bit more backbone - offers more body and roundness to the beverage. Try both versions to understand the different contributions these two base spirits can offer to the same cocktail.