1995 Ford Taurus heater core?

I'm afraid there's not really a way around replacing it.
Some may suggest a stop leak product, but there's really no guarantee it will work.
You can buy a manual (chilton/haynes) to get the detailed procedure to replace a heater core.
It involves removing the dash, which is a time consuming job.
A shop will likely charge you around $500-600 to replace it.

Just adding to RenaudTN's post. Hope you don't mind?

HEATER CORE
NOTE:Vehicles may have an aluminum or copper/brass heater core. When heater core is to be replaced, use copper/brass replacement with new heater case seals. See Fig. 2.

Removal
Remove heater/evaporator case. See HEATER/EVAPORATOR CASE. Remove vacuum source line from heater core tube seal. Remove seal from heater core tubes.
Remove heater core access cover screws. See Fig. 2. Remove access cover and seal from heater/evaporator case. Lift heater core and case seals out of heater/evaporator case.
Installation
If installing new heater core, transfer case seals to new core. Install heater core and seals into heater/evaporator case. Install heater core access cover on case. Install seal on heater core tubes. To complete installation, reverse removal procedure. Evacuate and charge A/C system. Refill cooling system.
HEATER/EVAPORATOR CASE
Removal
Disconnect negative battery cable. Drain coolant from radiator. Gently pull instrument panel away from right side of dash panel. See INSTRUMENT PANEL.
Discharge A/C system using approved refrigerant recovery/recycling equipment. Disconnect heater hoses from heater core. Plug heater core tubes or drain coolant by blowing coolant from heater core using low pressure compressed air. Disconnect vacuum supply hose from inside engine compartment.
Disconnect A/C lines from evaporator core. Plug A/C lines and evaporator core tubes. Remove instrument panel assembly brace to evaporator case bracket screw. Remove assembly brace. See Fig. 2.
Remove floor register and rear floor duct from bottom of heater/evaporator case. Remove nuts securing heater/evaporator case to firewall. Remove 2 screws securing support brackets to cowl top panel. Carefully pull heater/evaporator case away from firewall. Remove heater/evaporator case.
Installation
To install, reverse removal procedure. Evacuate and charge A/C system. Refill cooling system.
INSTRUMENT PANEL
Removal & Installation
Position front wheels in straight-ahead position. Disable air bag system. See AIR BAG RESTRAINT SYSTEM article in ACCESSORIES/SAFETY EQUIPMENT section. Disconnect negative battery cable. Remove steering column trim shrouds.
Disconnect all electrical connections from steering column switches. Remove cover from under steering column. Remove 4 bolts and reinforcement from under steering column. Disconnect parking brake release control motor from parking brake and ignition switch connector.
Disengage insulator retainer. Remove insulator. Remove 4 nuts and reinforcement below steering column. Remove 4 nuts securing steering column to instrument panel and lower column to front seat. Disconnect PRNDL cable (A/T models).
Ensure ignition switch is locked to prevent steering column from turning. Remove 4 instrument cluster retaining screws. Disconnect speed control cable and vehicle speed sensor (if equipped). Disconnect electrical connectors and remove instrument cluster. At steering column opening, remove one bolt securing instrument panel to brace. Remove one instrument panel brace bolt (below radio area).
Remove sound insulator under glove box by removing 2 push nuts securing insulator to studs on climate control case. Remove glove box door and compartment. Remove air cleaner housing, battery and battery tray. Disconnect wires of main wire loom in engine compartment. Disengage rubber grommet from firewall. Feed wiring into passenger compartment through hole in firewall.
Remove right and left kick panels. Disconnect wires from instrument panel at right and left kick panel sides. Remove screws on left and right sides of instrument panel.
Pull up to unsnap right and left speaker opening covers. Remove speaker covers. Working through steering column and glove box openings, reach under instrument panel and disconnect electrical connectors, vacuum hoses, A/C-heater control panel cables, and radio antenna cable.
Support instrument panel. Remove 3 screws attaching top of instrument panel to cowl top. Disconnect remaining wires. Remove instrument panel. To install instrument panel, reverse removal procedure.