We are traveling to Paris the first of April and I am wonder what the weather is like from the 1st to the 20th
In 3 weeks you will surely have a few nice days, but I would prepare for cold and wet. Fortunately it's Paris, not the countryside, and you can always duck in to a cafe or museum based on the weather.
I don't know where you are from, but Aptil in Paris is a lot like April in New England. Among other things, that's very changeable.
Focus on layers you can add and subtract as conditions change: a rain shell that can double as a jacket, a scarf, hat and/or headband, lightweight gloves.
for what its worth (fwiw), i was there in mid March of 2012 and all i had was either overcast or sunny. Temps were mild/warm for where i come from. The sunny days were nice and on the warmer side, again from where i come from.
but as the previous poster mentioned, prepare for anything.