Strange I2C signals emitted from FPGA
So, the unwanted signals are synchronised but not perfectly identical (although that could be the scope) and about 1Vpp.

Crosstalk, perhaps?  Is there another synchronised but digital signal on a nearby pin or trace?  Do the unwanted signals disappear if you ground the pins rather than leaving them floating with pullups?

If you don't include the I2C module in the build, do the pins exhibit the same behaviour?  If you build in some GPIO attached to those pins and drive the pins high and/or low, is the unwanted signal overlaid on the driven logic level or does it disappear?

Also, doesn't the Zynq PS block have two I2C peripherals already?  Why aren't you using one of them?