Mix flour with 75 grams (approximately 2 1/2 ounces) of sugar. Melt butter, cut into pieces, and combine with milk and 1 egg yolk. Mix with flour mixture and knead quickly into smooth dough. Wrap into aluminum foil and refrigerate for 30 minutes. Roll out pastry and line tart pan with it, making 2 cm (approximately 3/4 inch) all around. Line with parchment paper and weigh down with beans. Bake in preheated oven at 175°C (approximately 350°F) for about 20 minutes.
Remove beans and paper from the pan and bake for another 10 minutes. Remove from oven and cool slightly. Whisk eggs with sugar until sugar has dissolved. Add creme fraiche, cream and lime juice, mix well. Spread cream onto pastry and smooth. Bake in preheated oven at 150°C (approximately 300°F) for about 50 minutes. If tart browns too quickly, cover with aluminum foil. Remove from oven, cool and refrigerate for at least 1 hour. Serve.