Binary stars are ubiquitous; yet it remains unclear how wide-orbit stellar companions influence the formation of hot Jupiters, particularly around M dwarfs. Here, we first report the discovery of TOI-5628Ab, a giant planet transiting a midtype M dwarf (M* = 0.36 ± 0.02 M⊙) every 4.34 days, accompanied by an associated white dwarf TOI-5628B (MWD = 0.59 ± 0.16 M⊙) at a projected distance of about 2500 au. Using TESS, ground-based photometry, and SPIRou radial velocities, we constrain the planet radius to 0.74 ± 0.04 RJ and mass to 0.09 ± 0.04 MJ, with a 3σ upper limit of 0.22 MJ. Building on this system, we further conduct a homogeneous systematic search for comoving stellar companions with projected semimajor axes between 100 and 10,000 au around all M dwarfs with confirmed giant planets with periods smaller than 10 days and radii larger than 0.7 RJ, as well as a group of field M stars with stellar properties similar to the planet sample, based on the stellar kinematics from Gaia DR3. We measure a stellar multiplicity of 34.2% ± 9.5% for M dwarfs hosting short-period giant planets, which is substantially higher than the fraction of 5.3% ± 3.7% for the field M stars by approximately a factor of 6. Our results suggest that wide-orbit stellar companions tend to promote the formation of short-period gas giants around M stars with masses 0.21 ≤ M* ≤ 0.64 M⊙, and high-eccentricity migration may play an important role in producing such systems.