High-power laser interactions with solid targets create an abundance of high-energy charged particles, resulting in the generation of intense electromagnetic pulses (EMPs), which are strongly pertinent to the target parameters. In this study, the characteristics of EMPs generated by relativistic femtosecond laser irradiation of double-layer targets composed of near-critical density carbon nanotube foams (CNFs) and an aluminum (Al) foil are investigated. The results demonstrate that the CNF double-layer targets accelerate proton energy by over 1.6 times compared to a single-layer Al plane target, thereby indirectly amplifying the EMP amplitude by over 3.6 times. The findings are beneficial to gaining insight into EMPs induced by femtosecond laser coupling with near-critical density targets and open a new avenue to achieve tunable EMPs by managing the material and structure of the target to optimize the coupling efficiency between the laser and solid targets.