Turned on my wipers and they both worked and then the passanger side just made a pop sound and stoped , but the driver side is still working?

There are nuts on the wiper arm posts under plastic caps[ if still there ] they looen sometimes and the arm won't move turn off the wipers so the 'park' and check the nut for tightness - should be quite snug. it that dosen't fix it then you have a linkage problem from the motor.

Unless there's something wrong with the linkages; which I can't imagine...
It almost has to be the nut is loose on the passenger side.

Make sure the wipers are off and the igition is off.
According to what you say, the driver's wiper is in the correct "parked" position.
On the passenger side wiper arm, pop off the plastic cover at the pivot point of the arm.
Underneath, there is a nut. Loosen the nut a little. Wiggle the arm while pushing the arm down. Hold arm in place and tighten the nut. Replace cover.

If that doesn't take care of it, you may have to remove the arm completely and check the tapered spline underneath. Either the arm or the post spline may be stripped. Maybe try a new arm, as the post will be more difficult to replace.

your wiper transmission has dislodged itself from the wiper arm on the passanger side...
Take hold of the passanger side wiper arm and see if it moves independantly ( not in sequence with the drivers side wiper arm).

You may be required to remove the fresh air intake valance and install a new ( used?) wiper transmission assembly...
What happens is the plastic cups on the wiper transmission wear out and pop off...
easy fix ya !

if the passanger wiper stopped working AND the drivers side is still working...one of two problems. the easiest is to pop off the black cap at the base of the wiper arm, under it you will find a nut. check to see the nut is tight. turn the wipers on and observe the post that the nut is on, if it is turning, then the nut needs to be tightened or the spline on the post or wiper arm is stripped. If the post is not turning, then most likely an arm on your wiper assembly has come off, remove the wiper arms remove the black plastic cowl and you will find the wiper arm assembly.
good luck. HTH

It sounds like the connecting arm that connects to both the driver and passenger wiper has disengaged on the passenger side. Pop the hood and look under the trim by the firewall and you may be able to see the wiper assembly. If not, then you'll need to remove the trim to get to it

check both door looms out for damaged wiring common problem on peugeots

Most likely the nut that hold the arm at the pivot has come loose, pop the cover off, out the arm back in poisition and tighten the nut down, should be a 13mm nut.

The problem is either the motor itself or the electric wiring to the motor. Check the motor connectors for corrosion under the hood grill near the windscreen. If they look ok get a set of jumper leads and connect them to the battery. Be careful not to touch them together. Then put them on the motor directly after disconnecting it if there is no instantaneous movement then undo the test rig because the motor is bad. If they work double check the connectors going to the motor its likely them.

Check the retainer nuts on the wiper arms. One might be loose. 

you may want to check the wiper arm and the wiper arm post the groves that hold it tight may be worn out