Starlight, I'm sorry I am just now seeing this. We have a Desert King fig tree and I have a friend who sells at the market next to me. He's given me about 40 pints that he couldn't sell in the last few weeks. Figs do freeze well, no problem with that. They are also DIVINE when dehydrated.
Now, as to the canning failures - if you go to all that trouble, you might as well be sure to do it right and not waste the figs. Start with new Ball/Kerr canning jars. Wash them with soapy water and rinse. I use a fig jam recipe at NCHFP - it was the easiest one I found. It is a long boil method with no pectin.
http://nchfp.uga.edu/how/can_07/fig_jam.html
You do need to use some bottled lemon juice in the recipe because figs are a low acid fruit and you need to boost that acid. Bottled because it is a guaranteed acidity. Tree fruit can vary. I dislike VERY much the preservatives in bottled so I use Minute Maid frozen juice in the freezer section. No preservatives but more expensive...but I consider it worth it.
Make your jam, boiling until nice and thick. Have a hot water bath canner ready at simmering around 180 degrees. I use a thermometer. Have the jars in that water to keep them hot. Fill your jars up to 1/4" headspace. Don't increase the headspace as it can increase chances for molding. Wipe the rims and threads with a wet paper towel. Even a speck of food can prevent a seal. Put on the ring and tighten JUST finger tip tight. Don't crank down that ring or the air can't escape.
Put in canner and turn up heat; bring to rolling boil, cover and process for 10 mins. Turn off heat, remove cover and let sit for 5 mins. Helps the jars to settle down. Place on dry kitchen towel away from direct draft. Don't tip sideways to remove water on lids. That can break the seal. Let cool for 24 hrs. Check seals, remove rings and check jar for stickiness, and put in pantry.
If you are shortcutting this, (not water bath canning or just flipping the jars to seal, or not wiping rims, or too much headspace OR reusing old lids) you could have problems. You can respond here or private message me if you need more help. Follow the directions and you should have no problem. A true seal is tight enough, that you need a can opener to pry it off. The lid won't bump off or slide off.