There is a very simple answer to this, which is worth looking into.
Firstly, constant torque is not what is needed, as film tension will vary as the takeup reel fills up (Tension = Torque/Reel_Radius)) . What we really need is something that gives a resonably constant tension.
Believe it or not, the (relatively) old-fashioned Permanent Magnet Brushed DC (PMBDC) motor has the characteristics to give us pretty much what we need. This is in contrast with the 'modern' brushless variety, that are extremely useful for many reasons in many applications, but not as far as I can see in this one. To use one of these for the take-up would probably need some kind of sensor/control system as talked about in this thread.
In a nutshell, the PMBDC motor has an inverse torque/speed characteristic. In other words, it provides higher torque at low speeds, and lower at high. This is just what we need. The reason for this is that the back-emf of the rotor decreases with decreasing speed, which increases the current it draws. Try stalling one of these motors with full voltage applied, and you could soon see smoke, but its torque will be at its maximum.
We, of course, only need to operate it at a fraction of its rated voltage (sufficient for the light tension we need), so that is unlikely to happen.
So, rather than using the motor as a speed-provider, we are operating it as a torque provider - when the reel is full, the speed is at its lowest, and the torque is at it's highest (dependent on the voltage we applied), and the converse is true when the reel is almost empty. Also, when the reel is completely empty, it will be free to rotate at a speed determined by friction/windage etc, but at a very low torque so it's speed will be limited, similar to that which we are used to with our old cine projectors.
For several reasons, the tension between empty and full will not be absolutely constant, but should be within about 10%. Also, unless you can get your hands on a precision multi-pole motor, I recommend using a low-cost one with an integral gearbox (about 10:1 - not critical). These can be bought on Ebay for less than £10.
Anyway, this is what I have been using for several years, and it fits my needs perfectly without any need for sensors, circuitry, or micro-controllers. Also, the operation is very gentle, with a virtual absence of 'snatching'. It just works!
For more detail and to check it out for yourself, look on Wikipedia for the difference in characteristics of brushed and brushless motors (and stepper-motors too, which are also inappropriate)
Hope you haven't found this too boring...