What was the reasoning behind using this particular structural shape? Why not just an ordinary I- or T-shaped beam, or a cylinder?
That modified X profile is called the Tresca section, named after the French scientist Henri Tresca who proposed it. The cross section is designed to provide maximum rigidity in a bar of fairly small dimensions and mass, and to minimize the effects of any slight bending that may take place when a bar is in normal use.
In the image, the lower surface of the central rib coincides with the bar's neutral plane, where change in length with flexure is minimum. The two lines that define the metre are engraved on the neutral plane. Flexure is to be expected, because during a measurement the metre bar is supported only at its two Bessel points (at 1/4 and 3/4 of its length) instead of lying on a flat table.