Were there any members of the French government who saw the potential for unrest in the 13 colonies to weaken Great Britain, and might have in anyway supported or influenced Patriot factions prior to the declaration of independence? (Similar to how popular imagination thinks about how the KGB/CIA would support political factions in other countries during the Cold War)
Well, kind of a member of the French government.
Pierre Beaumarchais had managed to make himself quite popular with his Figaro plays, but got into some complex intrigues- a court case over his earnings, and then there was a mistress of a duke....In any case, in 1775 he was trying to get back into favor by acting as a spy in London for the French government. He already had republican sympathies, began to hang out with John Wilkes, the radical politician. When the colonies broke into open revolt in 1775, he was approached by a representative of the Continental Congress, Arthur Lee, about the French government supporting the revolt. He had been sending very optimistic reports back to France about their success, and he then began prompting the French minister Vergennes to try to do something . Vergennes hated the British ( after all, France had lost a very bitter Seven Years War not too many years before) and agreed to help in a small but significant way. Beaumarchais then formed a fake company, Roderigue Hortelez and Co., which in the last half of 1776 got arms and supplies to the Colonists, funneled through their ambassador, Paris-based merchant Silas Deane. Those supplies were quite helpful in the Continental victory at Saratoga in 1777. It was after that victory that the French government took the colonial revolt seriously, and really began funding and supplying it, sending troops, etc.
Partially because the French wanted to keep the.1776 shipping secret , there was some confusion after the supplies were sent. The Colonists simply assumed they were gifts from the French government: but in 1778 Beaumarchais sent the Continental Congress a bill demanding payment for them. They do seem to have then paid for some of them, but when the French government began openly giving aid after 1778, there was a muddle as to who precisely owed whom for what. The French said they'd given three million livres, but only two were received. The Congress assumed the missing million had gone to Beaumarchais, told the French government that Beaumarchais had been paid once already, Beaumarchais disputed this, the French government as well. The muddle lasted for decades. Eventually it was established that the French government had actually secretly given Beaumarchais a million livres, the Spanish another million, and all that had been used to purchase those supplies. Unfortunately poor Silas Deane was caught up in the muddle. He'd incurred his own expenses in getting the supplies into the country, the Congress suspected him of profiting from it all and refused to pay: another merchant who did business with the Continental Congress and lived to regret it.
While Beaumarchais was in sympathy with the politics of the Colonists, at this point of course the French government was not. It was before the French Revolution, and the aristocracy was firmly in place. ( These were the French who had had Voltaire beaten up, not the ones who later would disinter him and move him to the Pantheon) The decision to back the Colonists was motivated out of Vergenne's wish to plague England.
An old but still useful account of Beaumarchais is over on JSTOR by Charles Millé: "Beaumarchais and the Lost Million"