Cut peaches in half, remove stones, and cut 0.5 cm (0.2 inches) thick slices.

Peel one of the limes in 7 long strips and place strips in a large bowl. Add the sugar, the juice of one lime, the peach slices and rosemary sprigs. Stir and set aside to macerate for at least 1-2 hours. 

Strain the peaches through a sieve straight into a small saucepan, and set aside the rosemary. You should end up with about 60ml (¼ cup) peach syrup. Try to leave as little juice as possible on the peaches.

Chop the rosemary you just removed from the syrup and set it aside.

Mix the grated zest and a teaspoon of sugar into the creme fraiche and refrigerate until ready to serve.

Preheat the oven to 180°C (355°F). On a lightly floured work surface, roll out the pastry just under 0.3-0.4 cm (0.1 inches) thick. Line a previously buttered 24 cm (9.5 inches) tart ring or pan with the pastry. 

Arrange the strained peaches in the pastry and bake for 25 minutes on the bottom rack of the oven.

While the tart is baking, whisk the cornflour into the reserved peach syrup. Simmer over a medium-high heat until it thickens to the consistency of honey (about two minutes), then pour over the peaches. Sprinkle the chopped rosemary leaves on top and return the galette to the oven for 15 minutes, until the pastry is golden-brown and the filling bubbling.

Remove from the oven and transfer immediately to a cooling rack. Leave to cool slightly, then zest a lime onto the tart, and serve with a bowl of the lime creme fraiche on the side.