You can say american permission matters more since its bit difficult to get. Logically you need OEM & french approval to integrate anything other than french origin on Rafale.It's mostly American permission that you will need. Did you need British permission to integrate them to the Jaguar?
And if you ask the Americans while you have aircraft procurement projects, they will refuse because they'll see it as a incentive to buy one of their aircraft instead of what the IAF wants. So keep them on the Jaguar for the time being, and look for integration on other platforms in, say, 2035 or so.