
Starter Click
The click from the starter motor is the starter solenoid/starter relay trying to tell you that it does not have the energy to turn the starter motor (which also turns the engine over to help start it).
The starter relay/solenoid is 'piggy backed' onto the starter motor and they are usually installed and removed as as a single part.
Battery
The main cause of the Citroen C3 starter motor click, click is due to a worn out car battery. Your Citroen C3 needs a reasonably well charged and good battery to turn the starter motor. A discharged or failing battery won't give enough energy to the starter solenoid when you turn the key. Instead of turning the engine over, the solenoid just clicks. During the winter months the cold temperatures affects the battery electrolyte more than in the warmer summer months. You may find a battery that performed well in the summer will only click the starter motor in the winter. This is a good sign your battery is no longer at its best.
Recharge
The C3 battery may just need a recharge if it has been left to discharge. This discharge could be due to just leaving the car for weeks without starting. Remove the battery from the car and charge it on the garage with a 12v car battery charger (amazon have them).
Old
Your C3 battery may be very old, over 5 years and it may not be at its best. You could be due to replace it. If the charging described above produces no benefit and it is old, then now would be the time to replace it. Find a replacement at Euro Car Parts by registration number or model and year of your C3.
Loose terminals
Loose battery terminals are a cause of the 'starter relay click' on a Citroen C3. The two battery terminal clamps should be tight onto the battery. If the terminals are not tight enough onto the battery they can heat up and cause damage. They will eventually cause the click click sound. You can remove the connections from the battery to clean-up the battery post and the connections. Make sure the negative nut and bolt is tight and the quick release positive it also making a firm connection.
Starter Motor
If battery and connections are good, your mileage is high, say, over 100k, the clicking from the starter could be down to a worn out starter motor. The brushes in the starter solenoid wear with use and it can often be cost effective to replace the complete starter motor in the Citroen C3 than just recondition the brushes. Getting the starter motor out of the car is difficult and time consuming so make sure your battery and connections are good before looking at the starter motor.
Recurring starter click problems
You find that charging the battery cured the solenoid clicking problem and the car starts and runs fine, but next time you try to start the engine you hear the click click click and not start. You can recharge the battery again and the click-charge-click cycle continues. This sequence of events could indicate the alternator is not charging the battery sufficiently. If you can charge the battery off the car with a dedicated car battery charger but the car can't charge the same battery, suspect the alternator. A quick voltage check across the battery terminals with the engine running should show around 14.4v or so. If you are not getting more than the voltage shown when the engine is not running, look to the alternator being faulty.