To make the crust, in a large bowl, combine graham cracker, sugar, and melted butter. Pour into a 9-inch springform pan and press the mixture into the bottom firmly. Refrigerate for 15 minutes as you prepare the filling.
In another bowl, add the strawberries and 1/4 cup of sugar and let the strawberries macerate for 15 minutes. Process the macerated strawberries in a food processor until smooth. Strain the strawberry puree and discard the solids.
Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the cream cheese and remaining sugar until smooth.
In a large saucepan over medium heat, add the cream cheese mixture, heavy cream, and strawberry puree. Cook until the mixture starts to bubble around the edges. Whisk in the creme fraiche. Remove the pan from heat.
While the mixture is cooking, put the gelatin sheets in a bowl of cold water and leave for 5 minutes to soften or "bloom."
Once the gelatin is softened, squeeze out the excess water and whisk the gelatin into the cream mixture until completely dissolved.
Strain the cream cheese mixture and pour the filling into the springform pan. Refrigerate the cheesecake for 8 hours or overnight for the filling to set.
When ready to serve, use a knife to loosen the chilled cheesecake from the rim of the springform pan, then remove the rim. Cut the cheesecake into slices. Top the slices with additional fresh strawberries. For neat slices, wipe the knife clean between each slice.