The 32-year-old has been without a club since leaving Maltese side Floriana last year and will now link-up in attack with fellow England cap James Beattie.
"We're delighted to have a player of Franny's quality on board," said Stanley manager Leam Richardson. "We've been looking to add experience to the squad and we feel he brings lots of that.
"In his career he's been involved in multi-million pound transfers and played at the highest level. He'll score goals for us.
"To have someone with his CV here is a massive boost for the club and I think it will give everyone a lift."
Jeffers scored on his one England appearance in 2003 - a 3-1 defeat to Australia. Beattie was also involved in that match.