Luton nearly broke the deadlock early on as Dean Morgan raced down the left and played the ball into David Bell, but his effort from six yards was palmed away by Boaz Myhill.
Minutes later Hull nearly took the lead as Jon Parkin broke through, but his shot from 18 yards went straight at Beresford who palmed the ball away.
Soon after Danny Mills came within inches of putting Hull into the lead after making space inside the box, but his left-footed shot was cleared off the line by Kevin Foley.
Morgan came close to putting the visitors ahead soon after, but his shot from the left-hand side of the box flew just wide of Myhill's left-hand post.
Craig Fagan nearly put his side ahead midway through the half, but the Hull man saw his volley from 18 yards whistle past Beresford's right-hand post.
Parkin should have put the home side ahead midway through the second half as Ian Ashbee floated the ball into the box from midfield and the Hull frontman rose to beat the keeper, but his right-foot shot from eight yards rose just over the Luton bar.
Luton were give a half chance soon after but Parkin couldn't convert his header from eight yards as it floated past Myhill's left-hand post.
Substitute France nearly put his side in the lead in the latter stages, but Beresford pulled off a great save after first saving Mills's free-kick from 20 yards.
Hull had Mills to thank late on as he flung himself in front of Morgan from close range, the Man City loanee deflecting the ball over with a great tackle.