The plane was a further development of Potez 43 family, tracing its roots from Potez 36. An airframe changed little from Potez 43, main difference were stronger engines. A prototype Potez 58 first flew on 7 March 1934. In September 1934 the first serial variant Potez 580 was flown, powered with 120 hp radial engine Potez 6B. There were built 80 of this variant. An air ambulance variant was also evaluated.
There were next built several small-series variants, differing with the last digit in designation. The second variant built in a significant series was Potez 585 - 108 built.
Mixed construction strutted high-wing monoplane. Rectangular two-spar wing, with rounded ends, supported with V-shaped spars. Wings were equipped with slats on 1/3 span. Closed cabin with three seats. Radial engine in front, with a Townend ring, two-blade propeller. Conventional fixed landing gear, with a rear skid, wheels in teardrop covers.

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