Wolf-359 (CN-Leo, GJ-406, Gaia-DR3-3864972938605115520) is a low-mass star in the fifth-closest neighboring system (2.41pc). Because of its relative youth and proximity, Wolf-359 offers a unique opportunity to study substellar companions around M-stars using infrared high-contrast imaging and radial velocity monitoring. We present the results of Ms-band (4.67{mu}m) vector vortex coronagraphic imaging using Keck-NIRC2 and add 12 Keck-HIRES and 68 MAROON-X velocities to the radial velocity baseline. Our analysis incorporates these data alongside literature radial velocities from CARMENES, the High Accuracy Radial velocity Planet Searcher, and Keck-HIRES to rule out the existence of a close (a<10 au) stellar or brown dwarf companion and the majority of large gas giant companions. Our survey does not refute or confirm the long-period radial velocity candidate, Wolf-359b (P~2900days), but rules out the candidate's existence as a large gas giant (>4MJup) assuming an age of younger than 1Gyr. We discuss the performance of our high- contrast imaging survey to aid future observers using Keck-NIRC2 in conjunction with the vortex coronagraph in the Ms band and conclude by exploring the direct imaging capabilities with JWST to observe Jupiter- and Neptune-mass planets around Wolf-359.