It's not about being timid, it's just that the French Navy is truly no match for the British.
In order to support the American independence, the French fleet had to toughen up and engage the British in the Caribbean Sea, but ended up being beaten like dogs, resulting in the loss of a great deal of control over the Caribbean. In the end, in order to preserve the sugar-producing base of Santo Domingo, later known as Haiti, they had to exchange North American lands ten times larger with the British.
Joseph would not make such a mistake again for the sake of supporting Mysore.
Exerting force in India was meant to drain the British, not themselves.
The most important thing for France right now was to develop industry. A huge amount of start-up capital had been poured into steel, coal, textiles, steam engines, and many other sectors, just when massive investments were needed for industrial expansion, they could not afford to waste money on warfare and cause the industry to stagnate.