The party wall separating my property from my neighbour’s is collapsing. However, my neighbour does not want to contribute to the cost of repairing the structure. Am I entitled to require them to contribute to these costs?

Yes. The law provides that you may compel your neighbour to “contribute […] to the repairs of the boundary separating [your properties] […]” (Arts. 663 and 667 of the French Civil Code).