Peugeot has the reputation as being France's most conservative automobile brand, though its 402 quasi-streamlined model of the mid-to-late 1930s was an exception. The new 203 was true to Peugeot form, however, its styling being largely derivative. Absent were features in the postwar styling air such as envelope bodies with flow-through fenders. In other words, the 203 was a "safe" design that would sustain Peugeot while the French economy completed its recovery from the war and then could move towards greater prosperity.
The 1948 Salon de l'Automobile de Paris was unusual in that it was held in late June and early July, rather than in the early fall, as was the normal case. The 203 was in production by fall and can be considered a 1949 model. Its most backward feature was the flat, one-piece windshield. It was also a fastback design, fashionable around the time it was introduced, but soon to be abandoned by most carmakers. Fenders are separate, though the front fender does extend back over part of the front door. Doors are hinged on the centerpost, simplifying the over-the-door fender feature that would have required more complicated hinging if front door hinges were on the cowling.
According to the link above, contemporary photos of early 203 rear ends are rare because Peugeot was somewhat embarrassed by the protruding gas filler cap. I include this picture because it shows the offending cap as well as the initial rear window, later enlarged.
Several years later, not much had changed.
Front fenders flowing over front doors reached production on 1939 Opels. Here the hinging arrangement was opposite that of the 203, both doors opening from the centerpost. Peugeot stylists were aware of these Opels as the 203 project was getting underway during the war.
The Wikipedia entry suggests that the 1942 Chevrolet might have served as inspiration for the 203 design. That cannot be ruled out, though its basic design elements were also present on the Opel pictured above. Seen here is a 1948 Chevrolet that differed from 1942, 1946 and 1947 models only in terms of minor trim details.
I include the 1940 Chrysler because the 203 has a similar, though wider, grille.