Beans (P. vulgaris) have closed blossoms and rarely cross pollinate. They have to exchange pollen. It is possible for bumble bees or something similar to open a blossom but it is a rare occurrence. At any rate you would not know until you grew out the saved seed.

The F1 seed looks like the seed of mother plant, because seed coat is maternal material. Only the germ inside the seed coat contains the mixture of two varieties.

The F2 seed will show a wide variation in seed coat colour and also in size. Exactly what you will get, will vary.

Planting close together does not guarantee you will get any crosses at all. Unless you are planning to grow every last seed from this year's plants you will miss a possible cross anyway, because the F1 seed looks like the seed of the mother variety.

You can make deliberate crosses, but it is not so easy with beans. It is easier with peas if you wish to experiment.