Francis played with the Redskins last season after playing with several other franchises in the first few years of his career. The 6-foot-5, 337-pound defensive lineman previously played for the New England Patriots, Miami Dolphins, Seattle Seahawks and Tampa Bay Buccaneers.
The Giants signed Francis and quarterback Alex Tanney on Wednesday. The Redskins cut the defensive tackle on Monday.
"When the team you were on didn't appreciate you, but the team you played against actually pays attention to the film," Francis wrote on Instagram, while tagging himself at MetLife Stadium in East Rutherford, N.J.
Francis also included a series of hashtags, including: "#ImaSeeYall[expletive]TwiceThisYear, #AndYourLogoIsRacist" and "#ThisIsMeLaughingAtYallBigMadInTheCommentsToo."
The Redskins' logo, and their team name, has been a hot topic for debate for years. The team has been known as the Redskins since 1933. Team owner Daniel Snyder has said that the team will "never change" the name.
In January, Oneida Nation representative Ray Halbritter released a statement regarding the Cleveland Indians' decision to no longer display the controversial Chief Wahoo logo on their uniforms in 2019. Halbritter mentioned the Snyder and the Redskins in the statement.
"Washington owner Dan Snyder needs to look at Cleveland's move and then look in the mirror and ask whether he wants to be forever known as the most famous purveyor of bigotry in modern sports, or if he wants to finally stand on the right side of history and change his team's name," Halbritter said. "We hope he chooses the latter."
Francis also hashtagged Oct. 28 and Dec. 9 in his post. Those are the dates that the Giants face the Redskins during the 2018 regular season.
The 27-year-old defender had 18 tackles in six games last season. He has appeared in nine games during his NFL career.