For 1,000 EUR you can buy a second hand Sony A7S (Mark I). I've reccently bought one as I'm an events photographer/videographer and low light is also really important to me. There's no better low light performance camera in this price range than the A7S. I bought mine for 880 GDP (1,000 EUR).
Here's a quick example of how it performs: https://www.youtube.com/watch?v=bEGpV845beQ