Weston-super-Mare have been drawn at home to League One Doncaster, while Warrington Town will entertain League Two Exeter in the FA Cup first round.
Other highlights of Monday's draw include sixth-tier Gosport Borough at home to Colchester, while Halifax will host Bradford City.
Seventh-tier Canvey Island will play two-time winners Preston if they defeat Havant & Waterlooville in a replay.
Ties will be played on 7, 8, 9 and 10 November.
|FA Cup first round facts|
|First-round winners will receive £18,000 in prize money||League One leaders Bristol City, the highest ranked side at this stage of the draw, are away to Gillingham|
|Northern Premier League Division One North side Warrington Town and Conference South team Gosport Borough are appearing in the first round for the first time||Three-time FA Cup winner Phil Neville made the draw along with Derbyshire FA's Community Coach of the Year Tammy Snape before a 300-strong audience at the National Football Centre at St George's Park|
"The chairman promised the lads a few quid if we got a league team so the players will be pleased," said Warrington manager Shaun Reid, brother of former Everton and England midfielder Peter.
Norton will face Conference Premier Gateshead after winning 2-1 at Shildon - the lowest-ranked team left in the competition - in Wednesday's fourth qualifying round replay.
"We wanted Port Vale, Crewe, Coventry, Sheffield United or Portsmouth but it was not to be," said Steve Beaumont, chairman of eighth-tier Norton.
"But we've had a great time so far in the FA Cup this season and we'll see how far we can go."
Isthmian League Premier Division East Thurrock United will fancy their chances of an upset away to League Two's bottom club Hartlepool United.
Lancashire part-timers AFC Fylde face a difficult tie at Plymouth, who are sixth in League Two.
Seventh-tier Maidstone United are away to League One opposition in the shape of Stevenage.
Conference North side Worcester have been drawn away to 1987 winners Coventry City, while Essex-based Concord Rangers are away to Mansfield.
Concord's Conference South rivals Bromley will be eyeing a place in the second round after being drawn at home to Dartford.
Blyth Spartans, who reached the FA Cup fifth round in 1977-78, entertain another past giant-killer Altrincham.
|FA Cup first-round draw|
|Notts County||v||Accrington Stanley|
|FC Halifax||v||Bradford City|
|Warrington Town||v||Exeter City|
|Dagenham and Redbridge||v||Southport|
|Port Vale||v||MK Dons|
|Havant & Waterlooville||v||Preston|