In a medium saucepan, combine the peaches, 7 tablespoons sugar, the lemon juice and salt. Cook over medium heat, mashing, until jam like, about 15 minutes. Let cool.
In a medium bowl, whisk together the cream, milk, remaining 3 tablespoons sugar and the cinnamon until the sugar is dissolved. Stir in the peach mixture and refrigerate for 4 hours.
Using an ice cream machine, process the peach mixture according to the manufacturers instructions. Transfer to an airtight container and freeze until firm, about 4 hours.