Sorry about the delay. I was away from home and did not have the exact details with which to refute your statements.
Let us take your points one by one
One actually, and Tipu Sultan was dead by 1799 anyway. If you know of others, please supply some names.
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Between 1788 and 1798, there were no direct French residents in India, due to the French revolution, and a bunch of policy changes in France. Most of the French-Indian communications were handled by French officers in the employ of the Indian rulers.
I would divide appeals to France into two categories. Before and after the Ripaud affair. After the Ripaud affair, no Indian ruler would commit himself in writing to the French seeking an alliance against the English, since the charade Ripaud played and its role in the death of Tipu precluded any written letters, and also damaged French credibility.
a) Raymond, a French officer who had raised a corps of 14000 troops in Hyderabad wrote to Comte de Malartic (the French governor of Mauritius, and a very active character), saying that the Nizam had raised his corps officered by the French as a counterweight to the British, whose influence he resented, and had informed him that he (the Nizam) would be prepared to act even more forcefully, if the French were to strike against British power in India.
b) Montigny, the ex-French resident with the Marathas, writing based on the communications he had received from the French officers in Maratha employ, wrote to the Directory in 1795-96 saying that both Shinde (Scindia) and Holkar were prepared to assist the French if the French would strike against the hub of British power in the west (Bombay). He also emphasised that the liberation of Broach from the British constituted a primary objective for the Maratha chiefs and that any French enterprise which included this objective would receive full support from the Maratha Peshwa as well.
The Marathas (here Montigny, in his memoir, is not specific who, among the Marathas, exactly made the proposal) made a proposal to Montigny that if the French could supply them ten thousand guns (for the infantry) and neutralise Bombay, the Marathas would invade the northern provinces and replace the English with other rulers. The Marathas would be compensated for this enterprise with the payment of Chauth (a tax which gave them 25% of the revenues of the state) in the states liberated from the English.
After the Ripaud affair, no one would write to any external power.
However, the anti British intrigues and appeals to the French did not end, or even diminish any.
a) Dubuc, the naval commander sent to help Tipu Sultan, returned to France in 1799. Apart from the messages of Tipu, he relayed to the emperor, urgent solicitations from Shinde, Holkar, and the Peshwa for French officers and equipment, along with bringing a verbal promise to act against the British, if the French would attack Bombay (but this promise by the Marathas was made in 1798, when it was believed that Napoleon would invade India). This is also corroborated by the messages sent by the Peshwa in 1800-1801 to the French through Dumoulin
b) In 1799, the British governor of Bombay, wrote to Henry Dundas that if Napoleon invaded there would be at least two powerful princes willing to support him.
c) The treaty of Bassein signed by the Peshwa Baji Rao caused a lot of heartburn among the Maratha chiefs. In 1801, Scindia, Holkar and Bhonsle sent word through several French officers (the whole thing has been summed up by Morenat in a series of memoranda to the emperor) pleading for French intervention. Howeveri, in 1801-1802, there was no one to listen to their pleas in France, and they were answered only in 1806 by letters from the French government (not sure who signed these, but they were forwarded by the French Ambassador of Persia, General Gardane) to Scindia, Holkar, and Bhonsle.
d) Morenat, a French officer who visited India between 1805-1807, returned home to report to the emperor that `Shinde and Holkar remain anxious to throw off the British yoke, and wish to enter into an alliance with France if we can land ten to fifteen thousand troops' He also relayed a request for `French officers of unimpeachable character' (Morena charged Perron, the French commander of Scindia, who fled the battlefield with treachery) to train their troops so that may face the English with confidence.
I have quoted a few easily available ones from books I have with me at home. Let me know if you want more. I can easily find another couple of dozen letters and communications from the French officers who served under the Marathas and the Nizam. The Marathas were intriguing against the British until the final destruction of the Marathas and their Pindari minions in 1817-1818. After that, with Tipu and the Marathas gone, the Nizam accepted final domination of the British. If the French/Russians turned up in force, the Marathas would side against the British. By 1808, simply put, the British were loathed by them.
Again, please provide a cite that the Indians were begging for Russian intervention.
No one was begging for Russian intervention, because the Russians (beyond one half hearted attempt under the Cossack hetman, Dmitri Orlov, in 1801) never showed interest in India. But we are talking of a Franco Russian alliance and its prospects here. Let us not change the terms of engagement.
Or, to put it another way, at the point we are talking about the King of Afghanistan received the first ever British embassy to Afghanistan and signed a treaty of alliance with Britain in the face of rumours of a joint Franco-Russian invasion.
The honest way to put it would be that Shah Shuja, who signed the treaty with the English and accepted the English embassy, was deposed seven weeks after the treaty and (later) exiled from his country for signing the `deplorable treaty' (those are Meredith Runion's words) with the English. The Afghans welcomed his opponent, Mahmud Shah, under whom the Afghans went back to hating the British. (See History of Afghanistan, Meredith L Runion). So - no, there was no love lost at all between the British and the Afghans.
But this hides a deeper problem with your theory. If, as you claim, the only thing that the Russians would be doing would be `to surrender to the British' on the Indian plains, why were the British so keen on signing an alliance with the Afghans? Surely, the terrain would be sufficient to deter any invasion?
Probably the most powerful remaining independent ruler - Ranjit Singh in the Punjab - was on friendly terms with Britain at this time and for most of his reign.
Ranjit Singh had a mixed relationship with the British, but that is irrelevant to this topic. At the point we are talking about (1808-1810), the Sikh empire did not constitute anything beyond the Chenab, and nothing south of Multan (including Multan). The Afghans had not even recognised him as anything but an upstart usurper, and were actively trying to recover (inbetween their internecine wars) Punjab from the Sikhs. They held all the territories west of the Jhelum, and Kashmir as well. At this point, Ranjit Singh was a growing, but still a minor power, and not the man who ruled from the borders of Tibet to Sindh thirty years later. The only power of real significance in the difficult territories between the Franco-Russians and India were the Afghans.
Okay, now we're just heading into fantasy land. Setting aside what looks like some wierd anti-British prejudice for a moment (the word is "British", not "Brits" - and rabbit holes? seriously?)
That is precisely what happened to the indigo planters during the sepoy mutiny (those that were not outright killed anyway), but that is a secondary matter. I was being colloquial, and referred to `Nappy' and `Brits'. But it is interesting that you take offence at the word `Brits' when you, the champion of evenhandedness, speak of the death of the French soldiers, who had just beaten Russia, even before the snows fall. It is illuminating. Kinda-sorta a bit rich, what?
the idea that any Afghan ruler would welcome the Russians passing through to establish themselves in India is simply absurd
Now it is you who is making assumptions. The Afghans saw themselves as the protectors of Islam in India. That is why Ahmed Shah Abdali attacked the Marathas, why Zaman Shah had tried to invade in 1798 - to restore northern India to a pliant Mughal emperor, from the wannabe usurpers - Hindu, Sikh and British. The Russians cannot expect to hold India, because they don't even hold (current) Kazakhstan properly at this point of time. But helping the Franco-Russians ruin British power in India is beneficial to them. By default, they will be the largest standing power left, and can expect to profit from fall of the British. The desire to restore India to Islam was still very strong, and up until Ranjit Singh conquered Peshawar, that remained the goal of the Afghan rulers.