My 2008 Ford Escape front brake locked up after changing the car battery, driving the car down the road the front left tire brake smoking.?

ID see how battery affected it, unless you somehow damaged an ABS cable. Try unplugging sensor from LF, If you have it (I go far. making an assumption,) If that don't fix it, do as Geo Metro sez; crack the bleeder, isolate problem.

You Don't need to replace rotor or pads or caliper, necessarily. Until it is Looked At. No one here has a crystal ball. Might have caught all in time.

The emergency brakes only are in the rear.

If the front brake is locking up you have a bad caliper.

Replace the rubber hose to the caliper when replacing the caliper and putting pads and rotors in the front.

Did you do something to pinch a BRAKE line when you installed the new battery?

The "emergency" BRAKE only works on the REAR wheels. It has no effect on the FRONT brakes.