Okay, so with an AD of 56 +4 (putting her right below top-ranked Garen at level 1 and right below top-ranked Skarner at level 18), to keep the same DPS...
ASpd at 1 = 35.302 DPS / 60 Attack Damage = 0.588
ASpd at 18 = 109.267 DPS / 128 Attack Damage = 0.854
Again, if the base AS is R and the scaling is S:
1) R + S = 0.588
2) R + 18S = 0.854
By elimination, we subtract 1) from 2) and get:
17S = 0.266
S = 0.0156
R + 0.0156 = 0.588
R = 0.5724
Giving Fransisca a base attack speed of 0.572 and an increment of 0.0156, expressed as a percent of 0.572 gives us 2.72%.
Attack Damage: 56 +4
Attack Speed: 0.572 +2.72%
Also I reduced the range on Bio-Energy Blast and Siege Engineer. Now Fransisca can still hit turrets from one back and a lane over, but can't hit enemy turrets from her own nexus.