Cook (65) started strongly alongside opener Nick Browne (60) as the hosts passed a century for the first wicket.
Tom Westley hit a fluent 64 before he was bowled by Ben Sanderson (2-79), who earlier had dismissed Browne.
Ravi Bopara (57 not out) and Dan Lawrence (44 not out) saw Essex to 335-3 at stumps.
Northants also conceded 45 extras, including 28 no-balls.
England captain Alastair Cook continued his fine start to the season with a half-century as Essex took control of the first day against Northamptonshire.