Magnifique, I would like to try baking a pie with such an oven!
With regards to the efficiency of the motion system, it occurs to me that your system only requires an occasional movement rather than a rapid movement for tracking purposes and therefore could conceivably build up the charge required for such motion over time. Such a build-up is inherently suited to renewable (solar, wind or thermal-recovery based) energy harvesting rather than the approach of powering the system from a separate electrical supply.
Secondly, the motion system appears to be single-ended and based upon a rope and a stepper motor. It would perhaps be useful to consider conversion to a more rigid system. I would suggest removing the line entirely, though if you want to keep it one possible option is that of steel wire, which can be had in a range of gauges and metallurgies. These are relatively very strong and inexpensive. Furthermore conversion to a closed loop would be desirable, ie. ability to turn in each direction. However, I would recommend a geared motor and a rotary track cut or milled in to a heavy base plate as a simpler solution with less parts and a higher probable efficiency. Ideally you could add a line-based system in case the motor has no power or breaks or something so people could point the thing manually in a worst-case scenario.
The use of a video/optical sensor path is inefficient from a processing perspective. While this is a great way to prototype an initial version, you are going to see issues around the presumption of a flat surface, the need for establishing a visual datum based upon peripheral codepoints, and distance estimates. Toward a more reliable, elegant and configurable solution one might suggest that a system of curves be established. Each row could become a single dimensional array with its own curve controlled by a single actuator (eg. a line) and then balanced off with springs, graduated mounting points, or some other counter-force, in order to effect inward curve at the elements closed to the end points. A major array would then separately angle all rows along the alternate axis. Done carefully this may be adequate for close actuation scenarios, though there is surely tradeoff between rigidity, precision, mechanical and control complexity, and efficiency. Assuming short distances, I suspect a simpler-is-best approach would be adequate. This could be combined with the critical element of a laser TOF ranging sensor to determine the subject range, which would inform the required algorithmic adjustment of the array geometry. In short, if you have knowledge of your own geometry, have known orientation relative that fixed point, and can before activation determine the TOF distance to your target, and have a GPS fix thus solar inclination at that moment is calculable, then it should be possible to track the target without the need for visual feedback.
In terms of temperature sensing, you can obtain remote temperatures using infra-red linear systems which should be effective.
In terms of safety, laser TOF ensuring no change in distance would ensure the subject is still within the programmed range and an intermediate object hasn't been introduced for combustion. Also, adding an IMS would be cheap and effective to detect events like being knocked over/moved and misalignment.
In terms of portability, it may be useful to use a collapsible carbon fiber structure derived from those seen in modern tents. Make the mirrors interchangeable so the collapsed form is tighter, they can clip on and also be readily replaced. If a concern is that the structure becomes too flexible, then consider adding more triangular structural elements, and potentially some form of self-tensioning system with a sprung tie-down.
In terms of gathering interest, not sure where you are based in France but I could suggest structuring the system as a public sculpture and holding events including eating food cooked by the system which could involve the additional sponsorship of local wineries, cider, etc. to garner social support.
As next steps first I would recommend mechanical prototypes for a single line operated adjustable curve system. Then I would recommend an array of those with the perpendicular axis on a stand. If necessary this could be prototyped as a fixed curve initially. Next the revised and compact stand (line-free), incorporating perhaps solar recovery for slow-tracking actuation. Finally an integrated control system with GPS, laser TOF distancing, IR thermal, IMS and the novel safety features.
Smiles from Sydney. I applaud your work toward the application of technology to social and environmental concern, we need more of this.