For renewal of Mexican driver's license in Cancun you need only your old license, your CURP (not required if previously recorded on your license), and proof of current address. The lines were very long for this earlier today so I'm going to try again in the late afternoon, per T.J.'s recommendation. It is my understanding that those who are permanent residents of Mexico cannot rely on their foreign license for permission to drive here. I got my Mexican license immediately upon being reclassified to permanent resident.
The lines were still long at 5 PM yesterday so I went back today at around 9:45 AM. The stars were aligned right, this time, and I was out, new license in hand, in 25 min, having completed a process that involved four lines. I chose the option of a renewal for five years to avoid having to repeat this process any time soon. The cost per year gets smaller the longer the period of renewal, but it was still expensive, at 2,101 pesos.