You can't look at historical data, since the timing of the tests matters, and there are other mitigation methods. That's why I specified a daily rate of at least 1000 (500k), and preferably 10k (5 million). I would imagine that for higher disease prevalence the lower 1000 metric is less likely to work, due to chaos and network effects.
Other than the timing issue, this metric also suffers from lag on the deaths, but I haven't found a better predictor.
I'm also talking about eradication when I quote these numbers - not mitigation. (New Zealand & Iceland status.)
They reduced the disease burden with lockdown. Another way to reduce it is with massive testing. Since we're not going to lockdown again, we have chosen to do massive testing in the US if we want to eliminate it.
It looks to me like France is doing about 20k tests per day (EDIT: 30-40k typically). Their 7 day average is about 33 deaths. So that's a ratio of 606 (EDIT: 1060).
Géodes - Santé publique France
I think they are currently unlikely to be able to eradicate the disease and fully reopen, at that testing level.
For Switzerland, they are currently performing about 5000 tests per day. And it looks like they may be increasing testing levels.
COVID-19 - Situation Suisse : Tests réalisés
At about 1500-2500 tests per death, I think they have a better chance than France of being able to return to near normal in the near future.
In both of these countries I suspect we'll see testing increase somewhat from current levels.
Obviously there is a big element of using tests efficiently - as I said, it's not all about the tests, of course. It's a broad term meant to apply to the whole apparatus.