AF and KL are notorious for making a lot more award space available to Flying Blue members than to partners. For the most part, what you see on delta.com is what you get. Across all airlines, there is generally not much award space available right now since nobody knows how many seats they will need for the summer.
If you are looking for transatlantic J specifically, new routes such as DEN may or may not have more space. Additionally, check cities that are not a Delta hub (e.g. DFW, IAH, or IAD) so that you are not competing with connecting passengers. If you are willing to transit Mexico or Canada, you may have luck checking flights out of MEX, YYZ, YUL, or YQB.
I honestly found zero AF J seats while researching this. I did see a few WS J seats on YYZ-CDG; is there a reason you need to fly Air France?
Hate to derail the thread, but I've been trying to find WS J via Skymiles forever. Really nice product over The Atlantic. What dates did you find it? I wasn't under the impression there was any space available for us.