Did Maria Theresa have any political influence in the French court or government?
No
Yes, briefly in 1672
Yes, she was highly influential
Yes, but it's unclear when
Answer
Maria Theresa did possess some political influence in the French court during the year of 1672. Her main sphere of influence was through her close personal friendship with Henrietta of England, who was the sister-in-law of Louis XIV and wife of his brother, Philippe, Duke of Orléans.
The Royal Revival: Exploring the Remarkable Reign of Maria Theresa of Spain