The former AFC Sudbury centre-half has become the Bantams’ second close-season recruit and follows on from the addition of Accrington Stanley defender Ben Richards-Everton, who will officially join on July 1.
French, 20, has spoken of his delight at landing an extended deal following a successful trial and Bowyer is urging him to seize the moment.
He said: “He is a good size, with good pace, and has a great attitude to take the opportunity we are giving him.
“I am looking forward to seeing him develop over the next 12 months.”
Barnsley duo Kieffer Moore and Ben Williams have been named in Wales’ senior squad for the Euro 2020 qualifying games against Croatia and Hungary.
Also included is Reds keeper Adam Davies – understood to be close to sealing a move to Stoke City – and Rotherham United captain Will Vaulks.
Moore and Williams received their first senior call-ups earlier this month for the Prinicipality’s training camp in Portugal and have made the cut for the qualifiers. But there is no place for Reds winger Ryan Hedges.
Leeds United forward Tyler Roberts also misses out, with the forward having undergone a minor knee operation.
Middlesbrough out-of-contract winger Stewart Downing, 34, is set to hold talks with Blackburn Rovers.
Rangers are also expected to speak with the ex-England player, with Sheffield Wednesday also linked.