What is the origin of the Montmartre mountain in Paris?
A clue is in the full name of the hill: 'Butte Montmartre'. A butte is an erosional feature in which a block of resistant rock overlies a less resistant layer. Erosion of the soft layer below causes the more resistant rock to erode as well by undercutting. This can lead to an isolated hill in a relatively flat surrounding.

The Montmartre hill itself consists of relatively resistant sedimentary rocks (can't find what exactly, although Deffontaines (2005) and De Wever (2002) hint at sandstones and shales) overlying soft marls and gypsum, which was mined until 1860, also contributing to instability of the butte (Deffontaines, 2005). Evaporite-diapirism, as mentioned by Spießbürger, might therefore have played a role as well.

Deffontaines, B., B. Fruneau, A. Prunier-Leparmentier, A. Arnaud, R. Cojean, E. Pajot, J. Rudant (2005) Urban instability revealed by DINSAR and SPN Interferometry: The Montmartre "Funiculaire" case example (Paris, France). Géoline 2005
De Wever, P., F. Guillocheau, J. Reynaud, E. Vennin, C. Robin, A. Cornée, D. Rouby (2002) Deux siècles de stratigraphie dans le bassin de Paris. Comptes Rendus Palevol