I am a fencer and it looks closer to an epee, rapiers usually have a + shape to the blade and are unsharpened but come down to a point and are made soley for piercing, Epee's are sharp on 2 sides for about 10 inches down each side, and sabers are single edged slashing and piercing weapons, all 3 are single handed though and you did a good job on it.
Actually, Rapiers came in all kinds of shapes.
http://www.thearma.org/Youth/rapieroutline.htm
And Epee's are modern sport weapons, So they never had any edges to begin with.
I am a fencer and it looks closer to an epee, rapiers usually have a + shape to the blade and are unsharpened but come down to a point and are made soley for piercing, Epee's are sharp on 2 sides for about 10 inches down each side, and sabers are single edged slashing and piercing weapons, all 3 are single handed though and you did a good job on it.