There is a good put in at Motts Run Landing for the entire section on River Road (Rt. 618).
Alternate put in options would be to park at Sunshine Ballpark (1200 Wicklow Dr, Fredericksburg, VA 22401) you can then carry down the gravel access road to put in above or below I-95 depending on how far you want to carry.
The other option is to park alongside Fall Hill Ave. near the Virginia Outdoor Center and put in right above the Falmouth Rapids.