The style in the second picture would be labeled Art Deco and the period would be 1920's and 30's. There are many similar chairs online listed as French Colonial or British Colonial Art Deco. Usually listed as easy chair, armchair, lounge chair, or the French term fauteuil.
The chair in the first picture looks a little more French Colonial but probably from the same period. The chairs pictured here are similar and are described as French Colonial with Art Deco and neoclassical influences. The seller says they are from the 30's.
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