For me, ^ is a modifier for “accents circonflexes” (êôî…). I have to hit the corresponding key twice to get the ^ symbol.
Since it is a modifier, it is not necessarily always handled like a symbol like ~ or ² (the latter being what’s bound to that physical key you’re interested in, in the fr layout)
To establish that your problem stems from the layout, try switching to fr; you’ll get ² in text fields for that key; try binding it in game, and using it. Odd are, it’ll work. I often bind stuff to that key in game, and most games i’ve tried it in recognise it.
If it does, then the next step will be finding a german layout for you with ~ or ² or anything sensible bound to that key.