The initially Havoverian King's German Legion was part of the British Army.
Did not their officers have the King's commission?
Even if so, that's a completely different subject. Were any German officers commissioned in the English army. Not that I've ever heard. Serving within the King's German Legend, of course.
It's not at all unlike the American "colored" units with the US army. Were there blacks serving with the army? Yes, of course. Where there ever any blacks commissioned within the regular US army? Not until after WWII when the "colored" units were eliminated and the army integrated.
To state that Germans, Frenchmen were commissioned in the English army/navy we need to know their names, date of commission, units served with, etc. We have all of that information with the Frenchmen that Smith commissioned to serve on his expedition to the Levant. If this was not unique, please provide the same information. If this did ever happen, other than by Smith of course, I presume that somebody would have mentioned it by now.
From what I've read, on the whole, the top English military leaders were extremely nationalistic and prejudiced, especially against the French. To have a Frenchman actually serving as a commissioned officer in the English army would not have gone unnoticed.