Bristol prop Sinckler made the last of his 68 appearances for country at last year's Rugby World Cup.
Northampton back-rower Ludlam also featured at the tournament, claiming his 25th and final cap in the third-place play-off with both missing out on selection during this year's Six Nations.
The pair's move to the three-time Champions Cup winners will end their England aspirations, with head coach Steve Borthwick unable to select players based with clubs abroad - although they may return in the future.
"They are two good signings who will complete our forward pack for many years," Lemaitre told AFP.
"They respond to the profiles we're looking for in our recruitment, we're trying to have higher expectations on mentality, behaviour and lifestyle of players like their impressive compatriot Dave Ribbans," he added.
Toulon, who won the last of their four French titles in 2014, head to Bayonne in the league on Sunday sitting fifth in the table with seven rounds of the regular season remaining.
