There is no published minimum. The investment must be substantial relative to what establishing this enterprise costs, which in a franchise usually means committing essentially the whole of the fee, build-out, equipment and working capital rather than a portion of it.
Proportion to this business, not to a threshold
The test is relative, and franchising makes the denominator unusually easy to establish, because franchisors publish disclosure material setting out the expected total cost of opening a unit. That figure becomes the benchmark against which the commitment is measured, and an investor who has committed close to the whole of it is in a strong position.
Money borrowed personally can form part of the investment where the investor is personally liable and the loan is not secured by the enterprise's own assets. Separately, budget for costs outside the investment: visa application fees published by the Department of State, professional fees for the immigration case, commercial and franchise legal review, accounting, and the operating losses that a realistic first-year plan should acknowledge rather than conceal.