The addition of fillers has been implemented in fused filament fabrication (FFF), and robust carbon fillers have been found to improve the mechanical, electrical, and thermal properties of 3D-printed matrices. However, in stretchable matrices, the use of fillers imposes significant challenges related to quality and durability. In this work, we show that long carbon staple fibers in the form of permeable carbon fiber cloth (CFC) can be placed into a stretchable thermoplastic polyurethane (TPU) matrix to improve the system. Four CFC sample series (nominally 53–159-µm-thick CFC layers) were prepared with a permeable and compliant thin CFC layer and a highly conductive and stiff thick CFC layer. The sample series was tested with single pull-up tests and cyclic tensile tests with 10,000 cycles and was further studied with digital image correlation (DIC) analyses. The results showed that embedded CFC layers in a TPU matrix can be used for stretchable 3D-printed electronics structures. Samples with a thin 53 µm CFC layer retained electrical properties at 50% cyclic tensile deformations, whereas the samples with a thick >150-µm CFC layer exhibited the lowest resistance (5 Ω/10 mm). Between those structures, the 106-µm-thick CFC layer exhibited balanced electromechanical properties, with resistance changes of 0.5% in the cyclic tests after the orientation of the samples. Furthermore, the suitability of the structure as a sensor was estimated.