Thibaut only arrived at the Leasing.com Stadium at the end of February, having previously featured for Irish side Cobh Ramblers before leaving the club in November.
However, he made just one appearance for the Silkmen, coming on as a late substitute in their 2-0 victory over Hampton & Richmond in the FA Trophy las month.
Avenue say the young forward, who has signed until the end of the 2023/24 season, will offer "some exciting pace" to their forward line as they look to avoid relegation from the Northern Premier League.
He featured for his new club for the first time last weekend as they defeated Stafford Rangers 1-0.
That result leaves them level on points with Basford United, albeit still in the relegation zone due to their inferior goal difference.
Photo credit: Ireland Football
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