Heat cream, geranium leaves, and sugar in a metal bowl set over a pot of simmering water, stirring until sugar is dissolved and cream is hot but not boiling, about 5 minutes. Remove from heat and cool slightly, then chill until cold, about 45 minutes.
Pour cream through a sieve set into a bowl and discard solids.
Beat together cream cheese and cream in a bowl with an electric mixer until thickened (cream should not hold peaks), about 2 minutes.
Divide blackberries and blueberries among 6 bowls or parfait glasses and top with cream.
