The boost in both airports was achieved despite two strikes conducted by French air traffic control workers during the month which led to the cancellation of 26 flights.
Manchester saw strong growth to a number of destinations, including Madeira, 49%, Cape Verde, 40%, Malta 33% and France 27%.
Meanwhile, Stansted has reported its 26th consecutive month of year-on-year passenger growth with load factors at 87%.
In the 12 months ending May 2016, the total number of passengers using Stansted grew to over 23.3 million, an increase of 9.3% over the previous year and the highest annual total since July 2008.
Elsewhere, East Midlands airport, posted a 4.5% increase in passengers in the month, driven by healthy numbers travelling to Spain and the Canary Islands.
Bournemouth airport saw a small drop in passenger figures but core sun markets, including Spain, Portugal, Canary Islands and Cyprus, all saw passenger numbers rise.
Charlie Cornish, chief executive of Manchester Airports Group, said: "Industrial action in France is having has an unacceptable impact on travellers using our airports.
“Just the additional delays in May cost airlines and passengers at MAG airports about half a million pounds.
“But this was the 50th such event over the last seven years, so across UK airports as a whole this adds up to considerable hassle and extra cost for airlines, airports and passengers.
"European airports operate in a complex network which means this avoidable disruption in France has significant knock-on effects to operations everywhere else.
"Ahead of what is set to be the busiest summer on record for UK airports, it is vital that European and national agencies work together to find ways to reduce the impact of strike on passengers and airlines.”
