In a way, it's betrayal, in another it's not.
If they had killed Hawkwood, they could've either followed his troops back to the 2nd brigade or captured and interrogated them for the general direction they're in. The only way for that to be avoided would be if they all kept mum about it or instantly scattered and deserted, never returning .
So it's not a question of 'If' they could've found the English without them, it's a question of 'when' they would've found them, and how much of a delay killing Hawkwood's men would've cost them in finding the main unit and whether that delay would've helped the English or French more.
On the other hand, both sides want a major battle to take place, though in different situations and at different times. So if him telling them would benefit their plans to beat them in one battle, it's very good as well.