The supported floor is 120 square feet of living space. 2x8 joists 16-inch on center at 10 feet of span and terminated and blocked on the beam, is a conservative sizing appropriate for living space and a deflection value of less than 360 and live load of 40+ psi.
You effectively have a field constructed beam 3-2x12 (6x12 nominal) over a 12-foot distance, which is correct for that span in most framing, even as a central beam (technically this could carry twice the floor span). The unknown question is how does that transfer weight to the ground? If the beam directly ties to the foundation, and transfers load to the footer, its very unlikely to fail. I am not a structural engineer, and having your plan reviewed by one is the best idea.
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