Leaking heater matrix
If the carpet is constantly wet in the footwell and you lose coolant slowly, no doubt, the heater matrix (the actual heating element) is leaking. There are two pipes crossing the bulkhead behind the engine, on the right side. Look up beneath the lower trim panels in the cabin: the pipes go through a black box, the valve you open and close by turning the red-blue control knob on the center console. If the valve is opened, the hot coolant flows through the heating element, transferring its heat to the air blown through it.
The heater matrix is quite similar to the coolant radiator, only smaller. Their possible failures are also very similar. Small holes can be soldered or filled with a special brass-like putty used to repair leaking radiators, cracks of the plastic parts can be repaired with epoxy glue. The metal radiator and the plastic head with the two yellowish pipes can separate and leak water, these can be glued back and sealed (clean the surfaces first, let them dry thoroughly and use bathroom silicone; there are two versions, the usually transparent one used for fitting appliances is stronger than the colored one used for aesthetic purposes). But you'd better track it down and repair locally than to use a fluid stopping liquid like Holts Radweld; such liquids can cause damage in other places in the cooling system, clogging and blocking small passages or the radiator.
Or you can vote for a replacement radiator, possibly from a salvage yard. The question is whether a salvaged matrix is in a better shape than yours currently is. The inner end and the sides of the matrix are covered by a spongy plastic. This plastic becomes sticky and peels off easily when old. So, if this covering is still intact, there are no visible signs of rust and coolant residue, the radiator and the plastic head don't fall apart easily, you have probably found a good matrix. Fill it up with water and check that it stays inside.
To replace it, you have to drain the coolant first (with a cold engine, for sure). Place a bowl (capacity: at least 7.5 liters) beneath the radiator and loosen the clip on the bottom hose. Turn the heater knob to the hottest position. Remove the filler cap. As the coolant starts to flow out, remove the bleed screws: one on the top of the radiator, opposite the filler neck, one before the thermostat on BX 16 and 19 and one behind the engine (older 14 engines have it on the hose leaving the de-aeration chamber; older 16 and 19 engines on the hose returning from the heater matrix through the bulkhead, just behind the right side of the engine; newer 16 and 19 engines, including the GTi in the center of a pipe crossing right behind the engine).
On right-hand drive cars you have to remove both steering column shrouds, unbolt the column mountings, separate the universal joint and withdraw the upper steering column. On left-hand drive cars it's much easier: simply remove both gloveboxes.
Put a smaller container and a rag underneath the pipes. Undo the four screws on the heater tap, two screws retaining the matrix in the heater and, from underneath, one bolt which retains the tap to the whole heater unit. Prise apart the retaining clips around the yellow panel of the matrix. Withdraw the matrix carefully, as soon as it appears, pull by the unit itself rather than by the two yellow pipes. If you find that some control links are blocking your way, detach them. When refitting the new matrix (or the old one repaired), you'll have to struggle a little to pass the base of the yellow pipes over the tap—Haynes suggests detaching the coolant pipes, removing the tap, disengaging and removing the control cable, however, I did manage without any further disassembly.
To refill the cooling system, reconnect the bottom hose, leave the heater in the hottest position and fill in the water-antifreeze solution (as required by your climate) through the filler neck. After 6 (BX 14) or 6.5 liters (BX 16/19) slow down and keep an eye on the bleeding holes. As soon as the coolant starts to emerge through one, close that one. Top the system up to the standard level, run the engine in high idle while the fan cuts in and out, wait for the coolant to cool down again, then check and correct the level if necessary.