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.

Probably the same reason there are french imperial eagles in British museums.

Not sure, but there's also a Van Gogh in that 3D collection, you could ask the same question for that one.

The museum helpfully has a "Provenance" tab that gives you the answer to this question. (the answer in this case is market capitalism)