Louis XIV’s favourite colour was flame, an orangish-red which worked well with his self designated title of ‘The Sun King’. Louis wore it frequently.
Maria Theresa is handed over to the French and her husband by proxy, Louis XIV on the Isle of Pheasants
The French court was all about gaining the kings favour, and a good way to become his favourite was to wear his favourite colour, thus it’s frequently seen in garments and trimmings in 17th and early 18th century portraits.
Women wore it in ribbons and feathers:
La Grande Mademoiselle, Anne Marie Louise d'Orléans Duchesse de Montpensier by Louis Ferdinand Elle, 1640
Portrait of Françoise-Marguerite de Sévigné, Comtesse de Grignan attributed to Pierre Mignard
La Grande Mademoiselle, Anne Marie Louise d'Orléans Duchesse de Montpensier by Louis Ferdinand Elle ca. 1650
Or wrapped around their body in wraps:
Henrietta of England, Duchess of Orléans, oil on canvas, châteaux de Versailles et de Trianon, studio of the Beaubrun brothers
Men wore it as bows around their neck:
Louis Charles de Lévis, Pierre Mignard, 1675
Or as sashes tied around their torsos:
Antoine Nompar de Caumont, duc de Lauzun by Alexis Simon Belle
Whole interiors were done in it, and family groups wore it as jackets and robes:
Louis of France, Grand Dauphin, and his wife Maria Anna Victoria of Bavaria with their three sons- Louis, Petit Dauphin, Philippe (later King Felipe V of Spain) and Charles, Duke of Berry by Pierre Mignard 1687
If you didn’t like flame, but still wanted to kiss up to the king, inflicting it on your children in large quantities was always an option.
They could wear it as historical fantasy dress:
A young Mademoiselle de Blois, Marie-Anne de Bourbon, daughter of Louis XIV and Louise de La Vallière, by Pierre Mignard
Or pseudo-classical short clothes:
Élisabeth (Isabelle) d'Orléans, Duchess of Guise with her son by Mignard, 1672
Or stiff, old fashioned dresses with flame rosettes:
Elisabeth Charlotte of the Palatinate displayed with her two children Élisabeth Charlotte d'Orléans, (future Duchess of Lorraine) and Philippe d'Orléans, (future Regent and Duke of Orléans) by Pierre Mignard
Even Louis’ neglected wife and his kids wore the colour:
Maria Theresa of Austria (1638-1683) and the Grand Dauphin (1661-1711) by Charles Beaubrun, 1665
Yep. Mid 17th century France was aflame.