I live in Spain since two years and am still learning that language. I relate very much with what you’re saying because Spanish is spoken very quickly and I still have a hard time understanding it. A few days ago was for example the first time I could jot down the phone number someone was giving me on a phone message without having to replay it over and over again !
Also, I don’t remember of when I learnt English, but with Spanish, I’ve come up against periods of time when I felt I wasn’t learning anymore. It was quite frustrating. And then suddenly, I had breakthroughs as when I started to understand the news on TV. That one was so, so great by the way …
I checked the website you mention, News in Slow French, and it seems to be quite neat. It’s to listen but you also have the text and it even comes with a few translations when you hover over it. Really nice resource. The man who speaks doesn’t have a French accent, but as a French native speaker, I can tell you that his accent is really not a problem (as it may sometimes be with other language learning methods).
Language learning is a long term thing. I am sure your listening is going to improve a lot in the coming weeks if you keep doing what you do. Hang on, ça vaut la peine (it’s worth it) !