What European country today is foreseen to be flourishing (in terms of investment) despite of the economic downturn?
It's all over the news, investors are fleeing Europe, inflation is rising, stock market is declining, geopolitical issues over Russia, and other more things affecting Economic downturn in Europe.
Consider looking outside of the Euro area. Maybe look at Brazil or similar expanding markets.
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I am not sure I recognise the Europe you are describing.
EU and Euro Zone economies have been growing at a respectable rate since September 2016 with Spain leading the growth pack. In fact as of July 2017, Spanish GDP was back to the level as it was pre financial crisis. You can read the data for Q2 and historical data as well as forecasts that shows annualised growth forecast of 1.9-2% across the region https://tradingeconomics.com/euro-area/gdp-growth
Outflow of capital in EU is partly due to huge investment by Europeans across the globe including Asia, South America, and North America. In general there is no evidence for “Capital Flight” from the EU and Euro Zone.
Unemployment in the Euro Zone is falling month by month, and although higher than pre-financial crisis, it has fallen in all major economies in the Euro Zone (even in Greece). You can see current and historical data in http://ec.europa.eu/eurostat/statistics-explained/index.php/Unemployment_statistics
Inflation in Europe is subdued which is one of the problems ECB is grappling with as they try to reduce quantitative easing. Average inflation in Euro Zone was 1.32% in July and 1.5% in August which is well below ECB target https://tradingeconomics.com/euro-area/inflation-cpi
European stock markets are no more or less volatile than others and are prone to geopolitical ebbs and flows. DAX has grown by 20% over the last 12 months, CAC40 also grew by 20%, and TR Europe is up by 31%. So in general they are heading north.
Depending on what you want to invest in, your risk tolerance, and expected returns there are plenty of opportunities in the EU including FinTechs, Pharmaceuticals, Manufacturing, and Property. You can invest outside of EU or more regulated markets such as UK and US (at least for now), where you can get better yield but you can also lose your shirt!!