A proportion of infantry (typically around a quarter) are armed solely with melee weapons, normally halberd-like pole arms.
At first glance this appears quite anachronistic for such an ancient civilisation. However, like the smoothbore musket, these are actually a sign of adaptation to straitened circumstances rather than of backwardness. Given the inability to mount a decent bayonet on their musket, the halberd was probably (re)introduced to provide a degree of protection to the musketeers. The halberd is basically a large lump of metal on the end of a hardwood pole, and so is an expensive piece of kit. Over time they have developed into a status symbol to reward the loyalty and bravery of troops. Only the best and bravest therefore tend to be so armed*, which also limits the number that are likely to go missing upon desertion! Halberds are also more effective than muskets in a policing role, and when putting down civil disturbances with minimum force, so have rightly earned their place as a useful weapon on Mars.
The typical Martian sidearm is a sword of some description. Steel swords do exist, but these are museum pieces and family heirlooms rather than a commonplace. Most blades are made from a laminate of bone, wood, leather and sinew. Blades come in all shapes and sizes, and can be extremely strong and flexible, holding a good edge if properly maintained. Even those of poorer quality are quite capable of causing dreadful damage and of severing limbs.
*This also helps to explain the ease with which Earth governments have been able to raise such good quality auxiliary forces. In essence, and initially unknowingly, they have entrusted each Martian recruit with a Prince’s ransom of steel in the form of a rifled musket and bayonet. It is little wonder that such “trust” is returned.