[2] On December 13, 2013, Franco was selected by the Tampa Bay Rays in the minor league phase of the Rule 5 draft.

Franco opened the 2015 season with the Bowling Green Hot Rods, going 5–6 with a 3.89 ERA and 47 strikeouts in 71+2⁄3 innings.

On December 10, 2015, Franco was selected by the Atlanta Braves in the minor league phase of the Rule 5 draft.

Franco split the 2018 season between the Double-A Mississippi Braves and Triple-A Gwinnett Stripers, going a combined 7–9 with a 3.85 ERA and 131 strikeouts in 132 innings.

[12] He made his major league debut on September 18 versus the Boston Red Sox, allowing one run over one inning of relief.

[21] He appeared in 40 contests for the team down the stretch, recording a 4.41 ERA with 94 strikeouts and 10 saves in 100 innings pitched.

In 2023, Franco made 52 appearances out of the bullpen, recording a stellar 0.95 ERA with 71 strikeouts and 9 saves across 66+1⁄3 innings of work.

In 61 relief appearances for the team, he compiled a 4-6 record and 2.34 ERA with 56 strikeouts and 20 saves across 57+2⁄3 innings pitched.