The deal in itself does not end the walkout - striking union members will have to be consulted and vote - but there were signs the movement was losing steam and employers said they expected a settlement within a few days.
Leaders from the FO, CFTC, CFDT and Unsa unions said employers had agreed to pay an annual bonus to staff to appease their wage demands and that many of the workers themselves wanted the conflict to come to an end.
"After consulting our members, we see these proposals as better than nothing," said Thierry Fressart of the CFDT's service sector wing.
The CGT union did not sign the accord, but said it would consult members. The strikers had demanded €200 ($160) per month pay rises.
President Nicolas Sarkozy had ordered police to the airports to replace striking workers and avoid delays, and air traffic remained normal in Paris Charles de Gaulle airport and Lyon Saint-Exupery.
An association representing airports which employ security staff welcomed the union's decision, and said agents would receive a €1,000 annual bonus, while negotiations on working conditions would start next month.
Workers had earlier met and voted to continue the strike through Monday, and were expected to meet again on Tuesday to decide whether to back the deal agreed by some of their unions or whether to carry on.