As Cherry says, no one knows what the weather will be like - a few years back we had the the hottest March on record in the UK (so much so, it was hotter than summer!), but we also get snow and icy winds etc in March here in the UK and the coldness is more 'normal'. I'm saying the UK to compare, as our weather is very similar to that area of France, although they tend to slightly warmer summers!
Personally, if I didn't have to go in March, I probably wouldn't. Even a month later should make a difference - April will be warmer and as Cherry says, you may catch 'Swing into Spring'. DLRP is great any time, but I think it's extra special when there is a theme to the parades etc. However, just plan carefully as you don't want to hit school holidays - I think there could possibly be a period of about 3 weeks in April where you can span European holidays with Easter. If you don't have to go in school holidays then I definitely wouldn't recommend. Also, bare in mind it's the 25th Anniversary next year so after 12th April, the new birthday celebrations will take place every day - so something extra nice to see, you'll miss this if you go in March (I think there may be some soft openings before, but guessing most things will start on 12th April?).
Or, failing that, go early May - much warmer (although not hot!), less chance of heavy rain/icy winds etc, and lighter nights. Steer away from very last week in May as that tends to be a UK school holiday, although often the quietest of the school holidays as the rest of Europe are at school!