The Princess of Béthune was probably Albertine-Joséphine-Eulalie Le Vaillant (1750–1789), who married Eugène-François-Léon, prince de Béthune (1746-1824). Mme Labille-Guiard painted this beautiful portrait of the princess where she appear very young and elegant.
<bdi><a href="https://en.wikipedia.org/wiki/en:Ad%C3%A9la%C3%AFde_Labille-Guiard" class="extiw" title="w:en:Adélaïde Labille-Guiard"><span title="French painter (1749-1803)">Adélaïde Labille-Guiard</span></a>
</bdi>
1784 <a href="https://www.wikidata.org/wiki/Q112148051#P571" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" style="vertical-align: text-top" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20"></a>
<a rel="nofollow" class="external free" href="http://www.pastellists.com/articles/labilleguiard.pdf">http://www.pastellists.com/articles/labilleguiard.pdf</a> p.6