The 31-year-old has been without a club since leaving Atromitos in December 2010.
Speaking about his latest acquisition, United manager Peter Houston expressed his delight at finally locating a left-back to boost his side.
"I have been looking to add a left-sided defender to the squad," said Houston. "Gregory has plenty experience and it is important that we add experience to our young squad but first and foremost he is a very good player who will provide extra quality on the left hand side of the park.
"The length of the contract is ideal for both parties. It will allow Gregory to get a feel for our club and gives us the opportunity to assess Gregory over a longer period."
The short-term contract has a clause which could see the Frenchmen's time at the club extended until the end of the season.