Pre freeze the ice cream container you will be using
Peel and dice the peaches, or if you want a smooth textured ice cream you can puree the peaches in a food processor.
Pour the cold heavy cream into a large mixing bowl.
Using either a stand mixer, or an electric mixer, uses the whip attachment and whip the heavy cream until it is very thick
Pour half the can of the cold-sweetened condensed milk into the whipped cream and with a spatula gently fold the mixture together, then add the remaining condensed milk and continue folding in until it is totally combined.
Add the diced or pureed peaches and gently mix until combined.
Pour the peach ice cream in layers in the cold container, adding the blackberries for each layer. The amount of blackberries to add is your preference. You can add a lot or a little.
Cover the pan with plastic wrap and freeze for 4 hours.
Keep the ice cream in an airtight container for up to three months.
Notes
Consider the container you are pouring the ice cream into. If you are using a glass container be very careful because of breakage. For continued storage, make sure to use an airtight container to keep your ice cream at its freshest.