It sounds like a problem with the starter motor or fuse.

Ask someone to listen under the bonnet, does the click come from the
starter motor? If so, than it sounds like the starter motor is the problem.
Most likely the brushes are worn-out.

If the click is not coming form the starter motor, than the click is from a
relay.
I don't know If the starter-motor is connected via a fuse in a Saxo, I have
just
looked up in the Haynes service manual for the ZX and I see there is no fuse
for the starter-motor.

Try to get hold of a Haynes Manual for the Saxo. There you can find all the
info you need about fuses. Perhaps the brushes can de replaced, the manual
for my ZX shows how to do that. Otherwise you have to fit a new or
reconditioned starter motor.

This manual can be purchased in any good book-store, or search the internet
to find an illegal copy in PDF-Format. Unfortunately I only have the Haynes
manual in PDF for the ZX, BX and Xantia.

Good Luck.