Bridges and Welsh, who both barely figured in City's promotion last year, spent the majority of 2008/09 out on loan. Windass did likewise in January after only 6 appearances in the first half of the season.
France struggled to make an impact after his injury lay-off, playing twice in the Premier League and a further five times in the cups. He's reportedly joining hometown club Sheffield Wednesday.
Brown added: "It won't take a rocket scientist to figure out which players haven't played a major role this season and if there was a chance to move them on, we'll exercise that right.
"Without mentioning names, I'm sure there will be more players moving between now and next season."
Those names could be Nathan Doyle, Caleb Folan, Peter Halmosi, Bryan Hughes and Tony Warner, all of whom failed to make double figures in starting appearances.
Will Atkinson, Steve Gardner, Nathan Hanley, Ryan Kendall and John Leonard have signed new one-year contracts, while Tom Cairney has signed for two years.
James Bennett, Joe Lamplough, Matt Plummer and Tom Woodhead have not had their contracts renewed.