Could these wires stop the alternator from functioning. As I have replaced the alternator and it still isn't outputting any current

Those wires should be connected to the Battery Monitor System (BMS). What happened to the BMS? 

I suppose that you had a fault with bms/alternator, someone had probably cut the wires so that is just charges at 13.4 constantly. This shouldn't stop it from charging on a ford, although not ideal.

 

 

 

Although that negative lead being off will stop it from charging🤪

Have you tried fully unplugging those wires at the alternator end just incase they are also shorting out on eachother, as that will stop it charging

On my wife’s 2010 Mazda 2 , disconnecting the two wires on the battery monitor system on the negative battery terminal causes the battery to charge constantly at 14.4volts. And causes the battery light to illuminate on dashboard. I know that’s a Mazda but it was a joint venture design with Ford (even though the body shape is totally different and uses different engine/gearbox) and it has a Fomoco alternator on it.   Take the plug out of the bms. Strip the wire ends and hold on the terminals.  Make sure you get them right way round.  Don’t touch them together, god knows what that might do. Perhaps the ecu has been designed so the alternator won’t charge if the bms is disconnected on fords . The bms is there to reduce emissions by reducing alternator drag on the engine. 

If you have a soldering iron you might be able to solder the wires back on the remnants of the wires in the plug