Woods was ahead of Franklin, 29, in the first two splits through 11 gates, but crossed the finish line in 108.47secs, just 0.42 seconds shy of top spot.
"It is my second world title in C1 and that means a lot," Franklin said.
"I was pretty sure Kimberley was going to go in ahead of me and she is probably getting annoyed at the number of times she slips in just behind me.
"She did an amazing run and she showed how good we are on this course as a nation and the depth that we have at C1. I am really happy for her that she has got the silver."
Types of Canoeingpublished at 16:58 British Summer Time 22 September 2023
16:58 BST 22 September 2023
BBC Sport
There are two canoeing Olympic disciplines; slalom and sprint.
Canoe Slalom is the ultimate challenge as paddlers tackle the excitement of white water rapids, testing speed, agility and precision. Paddlers must navigate a sequence of pairs of poles (gates) set up over rapids, waves, eddies and currents on a 250m stretch of white water.
Entry level to canoe slalom racing are generally held on calm water and the courses will be simple.
Canoe Sprint sees you race on a straight course, each boat in a separate lane, over three different distances: 200m, 500m, 1,000m.
Most paddlers enter sprint racing through a club, racing locally as novices and progressing to national regattas at junior and senior levels, where all paddlers are ranked within their classes.
For those looking to start racing and to find out the location of sprint meets, the British Canoeing, external.
Media caption,
BBC Sport Scotland's Laura McGhie took on the K2 Canoe Slalom in Glasgow