Jones connected in the fifth for his 25th homer, a towering drive that capped a five-run inning and gave the Braves a 10-1 cushion.
Francoeur had a run-scoring single in the third and a two-run double in the fifth - just before Jones' homer - that gave the 23-year-old outfielder an even 100 RBI. He drove in 103 last year, his first full season in the big leagues.
All that offensive support made things easy for Smoltz (14-7), who was lifted after the sixth with the Braves comfortably ahead. He gave up four hits and his only run on Cody Ross' homer in the second, which briefly tied it at 1.
The Braves, clinging to the faint hope of making the playoffs, came into the night 5 games behind San Diego for the wild card and 7 behind the first-place New York Mets in the NL East.
Florida turned in a performance befitting a last-place team. Alfredo Amezaga misplayed two fly balls in center field, letting one bounce off his glove for a two-base error and totally losing another against the dark sky, giving Kelly Johnson a gift double.
Byung-Hyun Kim (9-7) gave up a career-worst nine runs, allowing nine hits and hitting three batters in four-plus innings.
For good measure, the Marlins ran themselves out of another inning when Hanley Ramirez was struck in the leg by Jeremy Hermida's sharply hit grounder while on the basepaths, ending the third.
The Braves also had a couple of runners get tagged out. Andruw Jones got caught between third and home on a failed suicide squeeze, and Francoeur was thrown out at third trying to move up on Brandon Jones' sacrifice fly.
Jones, who was called up Sunday, still picked up his first career RBI.
The third of Atlanta's starters with that name, Chipper Jones, had three hits and a pair of RBI before he left the game.
BRAVES' MAGIC NUMBERS
7 - Mets' wins and/or Braves' losses before eliminated from NL East race
9 - Padres' wins and/or Braves' losses before eliminated from wild card race