Monet's gardens in Giverny in late May

They will be gorgeous.

And crowded.

I agree, they will be beautiful. We went in early May in 2007, during a hot spring; everything except the waterlilies was blooming. Also, we were there a day after a mid-week holiday. Hardly any crowds but the people there said the day before, on the holiday, it was packed. I was amazed how well groomed the gardens were, nary a dead blossom; they must come out at daybreak and work. Also, no bare spots, the tall flowers were underplanted with low growing flowering plants. Birds were singing, bees were humming, large old trees were shading the perimeter and there are benches to sit and admire the view. The house is also picturesque.

Use the giverny.org website. It has tons of information in English. If you want to know what's blooming:

http://giverny.org/gardens/fcm/calendar.htm

It is a wonderful day trip.