2003 Ford Focus low fuel light will not turn off

I suggest you read the vehicle owner's handbook to be certain what the exact function of the light is. You will need to know that in order to determine whether the light is warning you or is broken.

The fuel light usually warns the fuel level in the tank is low...

Principles of Operation
NOTE: When installing a new instrument cluster, the new instrument cluster must be configured. Refer to Section 418-01 .
The instrument cluster is a hybrid electronic cluster (HEC) which receives and outputs information using both hardwired circuitry and the controller area network (CAN) communication circuits.
It is very important to understand:

• where the input originates from.
• all the information necessary for a feature to operate.
• which module(s) receive(s) the input or command message.
• if the module that received the input controls the output of the feature, or if it sends a message over the CAN to another module.
• which module controls the output of the feature.

The instrument cluster carries out a prove-out when the ignition switch is turned from the OFF to the RUN position to verify the integrity of the warning indicators. The charging system warning indicator, the low oil pressure warning indicator and the malfunction indicator lamp (MIL) illuminate when the key is turned to the ON position, and then turn off when the engine is started. The seat belt warning indicator proves-out for 60 seconds and then turns off, or turns off when the seat belt is fastened. The following indicators prove-out when the key is turned to the ON position:

• door ajar warning indicator (3 seconds)
• anti-lock brake system (ABS) warning indicator (3 seconds)
• O/D OFF indicator (3 seconds)
• air bag warning indicator (6 seconds)
• brake warning indicator (3 seconds)
• door ajar warning indicator (3 seconds)
• shift up indicator (3 seconds)
• low fuel warning indicator (3 seconds)
• traction control indicator (3 seconds)
• check fuel cap indicator (3 seconds)
• passive anti-theft system (PATS) indicator (3 seconds)

Low Fuel Warning Indicator
The instrument cluster utilizes fuel level data supplied by the hardwired fuel pump module to control the low fuel warning indicator, which illuminates when the fuel drops to a pre-determined level.
Your best bet is to take this to the Ford dealer , unless you have Ford IDS - factory scan tool to diagnose this
Your best bet

Check cable which plugs into back of instrument cluster. Also fusible links.

if you know there is gas in it sounds like fuel sending unit in tank

with ignition turned on to 11 there are certain warning light that do stay illuminated but will go off when engine has started ie oil pressure/ charging/ m i l light /handbrake warning will go off when h/brake released so if battery is flat know anyone with jump leads?? could help you start ?

Is the engine oil level good?

It could be the voltage regulator for your instrument cluster is the problem.

In my opinion it sounds like a problem from inside the fuel tank but don't quote me on this. With multiple sensors and switches related to fuel movement throughout the vehicle you're truly better off having a professional deal with this, unfortunately it will cost a few dollars.

could be faulty float in fuel tank but try fuse first

that light is the engine warning light you should go and have your car checked over at a garage running very low on oil can cause some serious problems with your engine. you'll also have to go to a garage to get them to turn your light off.