First dissolve the sugar in 5 fl oz (150 ml) water over a low heat until all the grains of sugar have disappeared, then turn the heat up a little bit and simmer gently for 15 minutes, without allowing the liquid to evaporate.
Then remove it from the heat and leave on one side for it to cool slightly. To prepare the mangoes, slice them in half along the length of the stone on either side of it (and have a plate underneath to catch all of the precious juice). Now use a spoon to scrape all the flesh away from the skin, then place this into a liquidizer. Next, using a sharp paring knife, remove the skin from the flesh around the stone then scrape all the flesh from this into the liquidiser, leaving the stone and any fibrous threads behind.
Now liquidise the mangoes until you have a smooth puree. If you don't have a liquidiser or processor, place a plastic sieve over a bowl and push the flesh of the fruit through. Either way, this should yield about 1 pint (570 ml) puree. Then add the lime juice and the sugar syrup and combine thoroughly.
Next spoon out the creme fraiche into another bowl and whip it lightly till it increases in volume and thickness. Now use a metal spoon to fold the fruit puree into the creme fraiche, and place the mixture in the plastic box and place it in the coldest part of the freezer for about 2 hours or until it is beginning to freeze around the edges. Then, using an electric hand whisk, whisk the frozen edges into the middle, replace the lid and return it to the freezer for another 2-3 hours, then repeat the whole process. After that, freeze again until it is quite frozen.
Before serving, place the box in the main body of the fridge for about 1 hour. If you have an ice-cream maker, freeze-churn according to the maker's instructions.