googling...
strain gauges on carbon fiber
...gives some interesting results for integrating strain gauges into carbon fiber products. But, for the most part, the results lead to very high-end and state-of-the-art papers. Section 1.2 of the thesis "Strain Monitoring of Carbon Fiber Composite with Embedded Nickel Nano-Composite Strain Gage" gives a simple summary of various other approaches to strain monitoring carbon fiber structures. None of them seem very practical for a hobbyist (which I assume, perhaps wrongly, the OP is...)
For a simple approach, I'd suggest guessing where the locations of maximum strain may be located. Attach strain gauges at those locations and monitor them.
(If you have the technical capability, you could calculate where the locations of maximum strain may be located.)