Head-mounted electronic display device with lens position sensing

A head-mounted device may have a display with first and second pixel arrays that display content for a user. A head-mounted support structure in the device supports the pixel arrays on the head of the user. A left positioner may be used to position a left lens module that includes a left lens and the first pixel array. A right positioner may be used to position a right lens module that includes a right lens and the second pixel array. Sensing circuitry such as proximity sensing circuitry may be used to detect relative positions between the left and right lens modules and facing surfaces of a user's nose while the user is wearing the head-mounted support structure. Control circuitry may adjust the positions of the left and right lens modules using interpupillary distance information for the user and using information from the sensing circuitry.