Tip the strawberries, sugar and 100ml water into a pan set over a medium heat. Cook, stirring, for about 30 mins, or until jammy. Tip the cooked strawberries into a sieve over a bowl and leave to drain.
Soak the gelatine leaves in cold water until soft, about 5 mins. Put the drained strawberry juice into a pan (you’ll need about 500ml – top it up with a splash of water if needed) and heat until just simmering. Remove from the heat. Squeeze any excess water from the gelatine, then stir into the warmed juice until completely dissolved.
Line a 900g loaf tin with cling film. Remove the crust from the brioche loaf, then slice the loaf lengthways into long pieces to fit the tin.
Soak a brioche slice in the strawberry jelly, then use it to line the bottom of the tin. Spoon over some of the raspberries, blueberries and the cooked strawberries, then a drizzle of the jelly. Repeat with the remaining brioche slices, berries, cooked strawberries and jelly until the tin is filled, finishing with a layer of brioche. Cover with cling film, then press down firmly. Chill the pudding for at least 4 hrs, or ideally overnight.
To serve, carefully remove from the tin, cut into slices and serve with the crème fraîche on the side.