Ford Thunderbird 96 V6 3.8 Idle rough, smokes like big Diesel motor

Possibly a blown head gasket, letting coolant into the cylinders to be burned. White smoke is usually coolant burning. Have the engine's compression tested to verify.

blue smoke is oil burning, it is call blow by, where oil gets by the valve seals and burns

Are you getting white smoke or no smoke from the exhaust after failed start attempts?
When the FICM was replaced, did Ford check the glow plugs and injectors for proper operation?
Are you using an engine oil heating element or is the engine dead cold when this happens?
How long does the engine run the first and second start attempts before it stalls and dies?

they have a tester called a smoke machine might be cheaper to just replace it rather than have it tested

Maybe just that the motor is cold or there is moisture in the carbie
Diesles usually smoke when you first turn them on and let them idle

Put the car on ramps and set e brake.

Use engine hoist to lift engine weight off of car.

Remove mount to engine bolts, remove mount nut.

Lift engine just enough to remove mounts and install new.

Watch exhaust, fuel lines and transmission mount while lifting. They may have to be loosened or moved.

Gas or diesel having same problem, I'd start there to confirm fuel pressure . It may be pump running partially when cool, but when it heats up (the pump) it may be cutting out pressure wise. Not uncommon for a fuel pump to pump good when cold, then die once pump heats up from running. Still makes noise, but isn't supplying any or enough pressure.

FORD: 1995-96 CONTOUR, CROWN VICTORIA, ESCORT, TAURUS, THUNDERBIRD
1996 MUSTANG LINCOLN-MERCURY: 1995-96 CONTINENTAL, COUGAR, GRAND MARQUIS, MARK VIII, MYSTIQUE, SABLE, TOWN CAR, TRACER LIGHT TRUCK: 1995-96 AEROSTAR, BRONCO, ECONOLINE, F-150-350 SERIES, RANGER, WINDSTAR
1996 EXPLORER This TSB article is being republished in its entirety to include the 1995 4.6L Thunderbird/Cougar. ISSUE: After a 1-4 hour engine soak time, long crank times and/or long crank to start followed by a stall may occur on some vehicles. No further stalling or rough idle will occur after the engine is running. The long crank and/or stall may be due to the Idle Air Control (IAC) Valve sticking.
ACTION: Replace the IAC Valve with a revised IAC Valve if no Diagnostic Trouble Codes (DTCs) are present. Refer to the following Service Procedure for details.
SERVICE PROCEDURE

1. Perform normal diagnostics and correct any DTCs as required by referring to the appropriate year Powertrain Control/Emissions Diagnosis (PC/ED) Service Manual.
2. If no codes are present, replace the IAC Valve by referring to the appropriate model/year Service Manual, Section 03-14. Refer to the following Idle Air Control Valve Application Chart for proper IAC usage.
   
   IDLE AIR CONTROL VALVE APPLICATION CHART Model Year Vehicle Engine Revised Part Number PASSENGER CARS 1995 Escort/Tracer 1.9L F5DZ-9F715-BA 1996 Escort/Tracer 1.9L F6CZ-9F715-BB 1995 Contour/Mystique 2.5L F5RZ-9F715-AB 1996 Contour/Mystique 2.5L F6RZ-9F715-AA 1996 Taurus/Sable 3.0L 4-Valve F5DZ-9F715-DA 1995 Taurus/Sable 3.0L 2-Valve F5DZ-9F715-EA 1996 Taurus/Sable 3.0L 2-Valve F6DZ-9F715-DA 1995 Taurus SHO 3.2L F6DZ-9F715-CA 1996 Taurus SHO 3.4L F6LZ-9F715-AC 1995 Taurus/Sable 3.8L F68Z-9F715-EA 1995 Crown Victoria/Grand Marquis/Town Car 4.6L 2-Valve F5PZ-9F715-AA 1996 Crown Victoria/Grand Marquis/Town Car/Mustang 4.6L 2-Valve F6AZ-9F715-EB 1996 Mustang 4.6L 4-Valve F65Z-9F715-BC 1995-96 Continental 4.6L 4-Valve F5OZ-9F715-AB 1995 Mark VIII 4.6L 4-Valve F3LZ-9F715-AA 1996 Mark VIII 4.6L 4-Valve F6LZ-9F715-AC 1995 Thunderbird/Cougar 4.6L 2-Valve F5PZ-9F715-AA 1996 Thunderbird/Cougar 4.6L 2-Valve F6AZ-9F715-EB LIGHT TRUCKS 1995-96 Ranger 2.3L F5OZ-9F715-AB 1995-96 Ranger 3.0L F67Z-9F715-AA 1995 Aerostar 3.0L F68Z-9F715-DA 1996 Aerostar 3.0L F69Z-9F715-AA 1995-96 Windstar 3.0L F68Z-9F715-DA 1995 Windstar 3.8L F68Z-9F715-EA 1996 Windstar 3.8L F68Z-9F715-CB 1995-96 Econoline/F-150-350 Series/Bronco 4.9L F68Z-9F715-EA 1996 Explorer 5.0L F67Z-9F715-BA

blown head gasket. black smoke means that oil is getting into the cylinder.

Check the color of the oil if it looks like a chocolate shake you have a blown head gasket