Harrison fought through qualifying to reach the main draw at this year's U.S. Open, beating Ivan Ljubicic before falling in the second round.
Davis is unbeaten in 27 straight matches and recently won two ITF Futures events, the Junior Orange Bowl and the Eddie Herr Junior Championships.
The French Tennis Federation said veteran Virginie Razzano and 21-year-old Benoit Paire would receive its reciprocal wild cards to Melbourne.
Razzano reached a career-high ranking of 16 in 2009 but has dropped to 114 this year due to injury. Paire is ranked No. 152 and will make his Australian Open debut.