Plums vary in sweetness; taste the plums before adding sugar to the caramel if they are very ripe.
If you don't have kirsch, a splash of brandy or orange liqueur works well as a substitute.
This tart can be made ahead. Store the baked tart in the refrigerator for up to 2 days. Reheat gently or serve chilled.
For a gluten-free version, use a gluten-free flour blend in the Pate Brisee.