diff --git a/src/sage/combinat/free_module.py b/src/sage/combinat/free_module.py
index 639cec54ae4..fc8800ef830 100644
--- a/src/sage/combinat/free_module.py
+++ b/src/sage/combinat/free_module.py
@@ -1776,6 +1776,25 @@ class CombinatorialFreeModule_CartesianProduct(CombinatorialFreeModule):
         sage: S = cartesian_product([cartesian_product([F, G]), H])  # todo: not implemented
         F (+) G (+) H
     """
+    @staticmethod
+    def __classcall_private__(cls, modules, category, **options):
+        """
+        Dispatch to the appropriate class based on the input.
+
+        EXMAPLES::
+
+            sage: Q = RootSystem(['A',3]).root_space(GF(3))
+            sage: W = WeylGroup(['A',3], prefix='s')
+            sage: CP = cartesian_product([Q, W])
+            sage: type(CP)
+            <class 'sage.sets.cartesian_product.CartesianProduct_with_category'>
+        """
+        R = modules[0].base_ring()
+        Cat = ModulesWithBasis(R)
+        if any(module not in Cat for module in modules):
+            from sage.sets.cartesian_product import CartesianProduct
+            return CartesianProduct(modules, category, **options)
+        return super().__classcall__(cls, modules, category=category, **options)
 
     def __init__(self, modules, **options):
         r"""
@@ -1787,9 +1806,9 @@ def __init__(self, modules, **options):
             Free module generated by {2, 4, 5} over Integer Ring (+) Free module generated by {2, 4, 7} over Integer Ring
             sage: TestSuite(C).run()
         """
-        assert (len(modules))  # TODO: generalize to a family or tuple
+        assert len(modules)  # TODO: generalize to a family or tuple
         R = modules[0].base_ring()
-        assert (all(module in ModulesWithBasis(R)) for module in modules)
+        assert all(module in ModulesWithBasis(R) for module in modules)
         # should check the base ring
         self._sets = modules
         CombinatorialFreeModule.__init__(self, R,