Presumably the exact same thing they'd have done if they hadn't rolled out this Find My feature. They designed it so Apple can't tell where your device is, which means if anyone wants to demand this info from Apple, then Apple has to implement that tracking separately, which they could do regardless of the Find My feature's existence.
If Apple had access to the device data themselves, then that's a huge problem because governments can reasonably start issuing warrants for that info. The fact that Apple doesn't have it means nothing has changed on the governmental front.