The 20-year-old, who also won the first and fourth stages, benefitted from the three-man breakaway being swallowed up by the peloton in the final kilometre of the 147-kilometre loop around Northamptonshire.
Magnier timed his burst to the line perfectly to beat out Norway's Erlend Blikra and Ethan Vernon of Britain.
"I saved a lot of energy and in the end, I did my best sprint and the victory is super nice," said Magnier.
The Soudal Quick-Step rider will fancy his chances of adding another stage win on the flat 158 km final stage from Lowestoft to Felixstowe.
"Why not? We will try for sure but it’s already super nice to take three victories here but for sure we will try to go again for victory," added Magnier.
Williams remains in pole position to win the general classification with a 16-second lead over compatriot Oscar Onley and Mark Donovan 40 seconds off the pace in third.
Stage four
1. Paul Magnier (FRA/SOQ) 3hr 12min 09sec, 2. Erlend Blikra (NOR/UXM) at same time, 3. Ethan Vernon (GBR/IPT) s.t., 4. Matevz Govekar (SVN/TBV) s.t., 5. Rasmus Sojberg Pedersen s.t.
Overall standings
1. Stephen Williams (GBR/IPT) 18hr 02min 56sec, 2. Oscar Onley (GBR/DFP) at 16 sec, 3. Mark Donovan (GBR/Q36) at 40, 4. Tom Donnenwirth (FRA/DAD) at 41., 5. Joe Blackmore (GBR/IPT) s.t.
