Answer: No. The Ford C-Max joins many cars that are being sold without spare tires (“Automakers leave nothing to spare” in the LA Times). It has what Ford calls a “Temporary Mobility Kit”. This kit includes a compressor and canister with latex sealant. The kit is stored under the front passenger seat. Ford recommends a maximum speed of 50 mph and driving no more than 120 miles when a tire is repaired with the kit. Ford also warns users that the kit cannot repair punctures on the sidewall and is limited to 1/4 inch or smaller holes. The tire sealant has an expiration date and must be replaced after storing the canister four years. After using the sealant, the tire pressure monitor sensor and the valve stem must be replaced for the tire. The sealant canister is for one-time use on one tire only. The kit description and use is explained in the C-Max manual on pages 335-343.
Update: 9 September 2016
Most of the time, I carry a tire repair/patch kit with me rather than a full-size spare. However, I did purchase a C-MAX rim and full size tire for those trips when I travel far from available roadside assistance.
Andy Konyha, a C-MaxChat reader, purchased a C-MAX compatible wheel, tire jack from a pre 2006 Ford Taurus, two tire covers, a fold up lug wrench and a tire tote. The tire covers wrap around the tire/jack/wrench. The covered tire was then placed within a tire tote. I’ve included photos of his spare tire below.
I’ve stored my spare in the luggage area behind the rear seat (as shown in the photo below) and at other times strapped to the child seat hooks on the rear seat, with the seat lowered (see photo below for the location).