Historically, the festival has always run in May for 12 days, starting on a Wednesday and finishing on the Sunday the following week. From 2018 (and beyond), the festival will now run Tuesday to Saturday.
The 73rd (2020) Cannes Film Festival was scheduled to run 12-23 May 2020. On 19 March 2020, the Festival de Cannes announced that this year's event will be postponed due to the COVID-19 crisis. No new dates have been announced as yet, although the Festival optimistically suggested that the event may take place late June / early July.
The last festival was the 72nd (2019) Cannes Film Festival which ran 14-25 May 2019.
For more information, you should visit the official festival web site at www.festival-cannes.org.