The Cod Army had the first chance of the match with Bobby Grant finding Wes Burns, who tested keeper Colin Doyle with a fierce low shot.
Fleetwood's Jimmy Ryan went closest, hitting the bar after the break.
Despite a late goalmouth scramble Fleetwood could not find a winner and stay one place and two points above the Seasiders in the last relegation spot.
The result leaves Fleetwood with just one win from their past 11 games, while the league's lowest scorers Blackpool are without a win in three games and in danger of suffering a second successive relegation.
Fleetwood and Blackpool remain in relegation trouble after the near neighbours played out a goalless draw.