What would the consequences of an economy-wide 500EUR/tonne carbon tax be?
My sense is that €500 / t CO2 is on the low side. It would change behaviour but it would not substantially alter the economy.

Here are some sample calculations how the tax would affect prices in the transport, food and electricity. This is of course before producers and consumers have adapted their behaviour.

Plane trip London-Paris return 0.244 t CO2 = tax €122 (244% of ~€50 lowest available fare)
Eurostar London-Paris return 0.022 t CO2 = tax €11 (18% of €66 lowest available price)
(Source1, Source2)

Carbon intensity of food consumption in Germany (Source)
1.9763 t x 1.2 (20% carbon intensity of last mile as per report) = 2.372 t
2.372 t / year x €500 = tax €1,186 / year
The proposed tax would add 27% to the average consumer spending on food in Germany of €4.320 / year (Source)

Carbon intensity of electricity generation in EU: 300 g CO2eq / kWh = 0.0003 t / kWh (Source)
Tax / kWh @ €500 t CO2: 0.0003 x €500 = €0.15 / kWh

Average price of domestic electricity in EU: €0.22, of which €0.09 taxes (Source)
The €500 / t CO2 tax would increase the electricity price in Finland (€0.17 incl taxes) to about the level in Denmark (€0.30 incl taxes): €0.17+ €0.15 = €0.32.

In sum, while the tax would likely change behaviour the proposed level appears to be in the range of other existing taxes for many products (VAT in EU is 17-27%). Arguably credits would have to be given to some households for them to be able to effort this new tax on basic necessities (these are typically VAT exempt today). That said, certain carbon-intense sectors that are not currently taxed at all would experience an important impact. Aviation is an obvious one. It would be important to identify them and their potential substitutes to determine the qualitative impact that the proposed tax would have.