The straight-line (great-circle) distance between Manchester (UK) and Paris (France) is approximately 850 kilometres (528 miles).
This is typically measured between their major airports: Manchester Airport (MAN) and Paris Charles de Gaulle (CDG). Flight time is ~1 hour 20 minutes.
By road + Eurotunnel: ~1,000 km, 10–11 hours driving. By train: ~4.5 hours via London St Pancras (Eurostar).