Toss thinly sliced fennel with vinegar, sugar and salt in a bowl. Let stand for 20 minutes, turning once, until lightly softened but still crisp.
Heat oven to 300°F and warm split croissants cut-side up for 5 minutes. Transfer to a rack and cool for 10 minutes.
Mix mascarpone, lemon zest, lemon juice and dill gently until smooth. Drain the fennel and pat away excess pickling liquid.
Spread the lemon-dill mixture over the croissant bottoms. Divide salmon flakes over the spread and add the drained fennel.
Close with the cooled tops and serve promptly or refrigerate at 40°F or below until serving.