The current Covid-19 Crisis 2020 has hit the Eurozone in a highly fragile situation, with a weak and asymmetric recovery from the Great Financial Crisis, the Great Recession and the following Eurozone Crisis. These crises have also revealed the weaknesses of the macroeconomic policy institutions and strategies of the Eurozone based on New Consensus Macroeconomics (NCM). Applying a Kaleckian/post-Keynesian analysis of the demand and growth regimes to the EA-12 countries, we show that the internal imbalances within the EA-12 before the Eurozone crisis, with the polarization of current account deficit debt-led private demand boom countries, on the one hand, and of current account surplus export-led mercantilist countries, on the other hand, have been externalized since then. Most of the countries and the EA-12 as a whole have now turned export-led mercantilist. For an economic policy alternative favouring a domestic demand-led regime, we turn towards Kalecki's macroeconomic policy proposals for achieving and maintaining full employment in a capitalist economy by government deficit expenditures, in combination with redistribution policies in favour of labour and low-income households, assisted by central banks targeting low interest rates. This approach is then applied to the Eurozone, in order to derive a policy mix which should contribute to a more rapid recovery from the Covid-19 Crisis and to a medium-to long-run non-inflationary full employment domestic demand-led regime, on the one hand, and to sustainable catching-up of the periphery of the Eurozone with respect to the more mature centre, on the other hand.