Looks like you have both cucumber virus and leaf blight (the brown spots).
There's no real cure, only preventative measures. Aphids are the #1 problem, so plant aphid attracting plants nearby to keep them off your courgettes. I highly recommend you bag and bin the infected plants asap and thoroughly wash your hands and any tools/equipment you used. The infection spreads very easily.
Start fresh seeds and place them in an open, sunny area, but don't crowd them - air circulation is paramount - and net them with very fine mesh like fleece to keep the aphids off. You'll want to hoop this area so the fleece doesn't touch the leaves making it easier for aphids to touch.
Never overhead water susceptible plants as the dampness is host to these diseases.
Whenever you touch any of the infected plants you must always wash hands and tools to avoid continuous disease spreading, and if you're a smoker, wash hands before handling any plants.
Come fall, or the plant starts to succumb, pull and gather all leaves and stalks, bag and bin them asap. Never compost infected material.
Practise yearly rotation of these varieties (all the cucurbit family), always clearing up every last bit of their plant material.
Some flower plants are hosts to these diseases: some chrysanths, lupins, flowering tobaccos, sunflowers, some brassicas, peppers, chicories and others.
Tomatoes and potatoes are also very blight affected so watch for any signs of blight on these. Check John's Information area for suggestions on dealing with these.
Sorry this is so long, but it's a bad problem for anyone who gets these diseases, and it's not easy to be rid of them, if ever.