The provenance according to the Met:

>Henry II, King of France (until d. 1559);

>Carl August, Grand Duke of Saxe-Weimar-Eisenach, Residenzschloss, Weimar (by 1804–d. 1828);

>by descent to Wilhelm Ernst, Grand Duke of Saxe-Weimar-Eisenach, Residenzschloss, Weimar, later Schloss Heinrichau, Lower Silesia, Germany (now Henryków, Poland) (1901–d. 1923);

>his widow, Feodora, Grand Duchess of Saxe-Weimar-Eisenach, Schloss Heinrichau (1923–1929;

>sold in May, 1929, to Kahlert & Sohn);

>[E. Kahlert & Sohn, Berlin, 1929;

>sold on December 14, 1929, for $135,000, to Sir Joseph Duveen for Mackay];

>Clarence H. Mackay, New York (1929–d. 1939; his estate, 1939, inv. no. A-17;

>sold through Jacques Seligmann & Co. on May 15, 1939, to MMA).

Unfortunately, this does not answer "why did it leave France?"

However, the book "Merchants of Art, 1880-1960: Eighty Years of Professional Collecting" (1961) by the rather famous art dealer Germain Seligman offers this missing link:

>Parade armor of King Henri II, embossed, damascened and gilded. Later presented by King Louis XIII to Bernhard von Weimar.