1781A Or 1791A Ecu From France

Hmm, these coins were minted 1774-1792, so either 1781 or 1791 is possible. Unfortunately there are no differences other than the year for Paris (A), the heron mint mark under the bust was in use both years. And both years are about equally common, 1791 being slightly more frequent.

Looking intensely at the year, I think I can imagine a 9 more than an 8...

What makes you think it isn't?

It is KM 564.1. KM 572 is the regional Bearn issue with a slightly different inscription and different mint marks.

This is a good point. But there is also statistical variation above and below the official issue weight, and I may have seen on CCF somewhere that during those turbulent times in France, that variability was higher, though I don;t know if that applied to all mints and types.
I compared this example with the 3 or four 1791 examples from the Paris mint on CoinArchives and could not see any major red flags with design details, at least to my eyes, and given the state of the OPs coin. Letters like N with thicker diagonal strokes than vertical ones look OK. The V in NAV rides a bit higher than the letters around it in some of the other examples, but not all. I don;t know this series at all, can just comment on what I see

Valid point and a good observation there, @retiredkper. I agree that had the OP coin really had a weight of 30 g, that would be a red flag.

How much the weight might vary for silver coins before and after the revolution is an interesting question to look into (especially on a Monday morning when the alternative is to come early to work ). So I quickly gathered some statistics from the CGB site, 1784 ecus in stock (happened to be the year with most examples) and 1791 ecus sold and in stock (cgb.fr keeps the data sheets for all sold coins and is a great source to dig into when it comes to French coins!). The result looks like this:

1784 ecus (25 examples):
Weight range 28.42 - 29.69 g with an average of 29.24 g.

1791 ecus (67 examples; one outlier with a stated weight of 27.54 g excluded - misprint or unrecognized fake?):
Weight range 28.68 - 29.64 g with an average of 29.34 g.

A more thorough investigation should correlate with the degree of wear and perhaps also separate the different mints (the two heaviest 1784 ecus both weigh 29.69 g and are from the Perpignan mint - were they extra generous with the silver or did their scales need calibration?). Still, as expected, the variation is more downwards than upwards. The mints were keen to keep the weight of (gold and silver) coins within as tight limits as possible and flans that were overweight were "adjusted" by scratching off surplus material with special tools (it is very common to see these sometimes rather ugly adjustment marks on gold and silver coins from this era). I don't know how the revolution in 1789 affected the precision of the mint work, but the small sample above does not seem to support that precision should have become worse - on the contrary, the span is smaller for post-revolutionary coins, in spite of the sample being larger than the pre-revolutionary sample.

Well, now off to work!

This is extremely fascinating Thank you to every one for all the great info. Adds to my meager knowledge base.

Sorry to bring you bad news but a specific gravity of 9.255 is way too low to be the quality silver used in a genuine coin. This coin should be over 10.3.