I have done the CF twice from late April to late May / early June. Plan for rain, perhaps every other day. Get the Eltiempo.es+ app for your smartphone. It has the most comprehensive weather status and forecast information for Spain and Portugal.
Basically the weather during this time can be cold and raw in the early morning. If you are lucky, the sun pops out and warms things up to where you can take off outer layers of clothing.
In my experience, and using this app for forecast information, if the probability of rain is under 40%, there will be not appreciable precipitation, though the day might be cloudy and blustery. If the probability is from 40% to 60% there may be a shower or two. However, if the probability is over 60%, plan for significant rain during the day. The weather app has hour-by-hour forecasts.
Also, plan to encounter light but wet snowfall at altitudes over about 700 meters ASL. This includes the Napoleon Pass, Alto de Perdon, Cruz de Ferro, O'Cebreiro, and any other peak higher than about 700 meters. I have walked past Cruz de Ferro three times from mid to late April to mid-May (2013, 2014, 2016). I have experienced snow, to some degree, every time.
On my last walk through O'Cebriero (2016), I found myself in the midst of a brief but furious snow squall with a whiteout for about an hour. One could not see 30 meters ahead. The snow was gone as soon as I walked down a hundred meters or so, after the peak...go figure...
Pack layers. Add and subtract layers as needed. You warm up as you walk. As long as you keep your feet dry, and your head and hands warm, you will be fine.
Hope this helps.