The term les Agasses comes from old high german agaza which designates a magpie. Word annoyed, Where agache in Picard, or aguiasse in Bourguignon, and agasse in Occitan, is found in the 11th century in the French language.
But nothing to do with the verb to annoy, which comes from Latin adacidare then old French steel.
So do not believe that magpies annoy.