Monet's Gardens

If you have particular flowers you're interested in seeing, go when they're in bloom--you can research this on the internet, search on Giverny and the times to see specific flowers.

If there are not specific flowers you're that interested in, consider these points:

There have been numerous threads on this site re best time to visit Giverny, here's just one of those threads:
https://community.ricksteves.com/travel-forum/france/is-there-a-best-season-for-giverny

One might think mid to late summer, but unfortunately that's when hordes (literally) of other tourists will visit and the lines to get into the house and visit the lily garden (around the pond)will be their longest.

Some here prefer late spring or early fall, avoiding the summer. There's really no way to avoid the crowds and still have the flowers in bloom, but we found that arriving as early as possible in the day (assuming one is sleeping in Paris) was best, we arrived by 9:30 am and avoided some of the crowding but not by much, as the big tour buses start arriving by about 10 am.

The garden is closed for 5 months of the year when there is no colour in the garden. They therefore plan on having something to see for 7 months.

I went the first week of June, midweek and not in school holidays and despite arriving before they opened, within minutes of the gates opening, it was unpleasantly busy and you had to wait for others to move before you could take photos. Upon opening, we literally ran to the lily pond to get some photos with no people in the background. It had been a cooler spring, so the water lilies weren’t fully out. The rest of the garden was a riot of colour. It was difficult to photograph as there were so many gardeners weeding etc that most shots included several gardeners!

The weather can alter flowering by about 2 weeks, so this year, having had a mild winter and a hot May, the water lilies would have been out earlier.

There is no way the National Trust in the U.K. would let so many people into say Sissinghurst garden at the same time.

Here's a link to the Gardens' website. It has a page that shows the flowering calendar.

Early May has the green bridge with wisteria. Azaleas, tulips and forget me nots. Even taking the first train of the day from Paris there are crowds. I have considered spending the night right by Giverny. It is picturesque along the little road by the gardens. We travel in May so garden annuals in Paris parks have just been planted. Gardens in Paris and Giverny would be at their summer prime around early July. Unfortunately, it gets hot and more crowded at that time. We select the best weather day during our stay in Paris for the garden visit. Rain might cut down on crowds, but this is mostly an outside visit.

I’ve been twice. The first time was in mid-October, just two weeks before they close for the season. I arrived at opening time. It was beautiful. The second time was in mid-June. I arrived before they opened and had a strategy of going straight to the water garden before it got mobbed. Nope, it was very crowded. I suspect some tours are allowed in before the official opening time. Of course it was beautiful and I saw flowers blooming in June that were no longer blooming in October, but I preferred my October visit with less people. Both trips we done mid-week.

As the above posts mention, anyone considering going to Giverny should be aware of the very significant crowds. It was still worth it for us, but the huge number of big bus tours from Paris detract significantly from what the experience could be if it was possible to visit when the place isn't mobbed. Those who absolutely detest shuffling through gardens in what's basically a line, or standing in lines for the house, should consider this factor in deciding whether to go.

Also, some expect to see Monet originals at Giverny, and are disappointed to learn there are no Monet originals at Giverny (but there a lot in Paris).

As long as they are open, they have a lot of flowers. Even in automn (they usually close around 1st November)
Check on their website as all cultural monuments are closed right now. We hope they will be reopen by next March, which is usually when they reopen (end of March around Easter)
Even on the first day they reopen everything is in bloom.
June is really good for roses (they have a lot) and peonies, august for waterlilies.

Has anyone ever tried going later in the afternoon?

The "best" time to go is when they are open, lol!! I've been in April, May, September and October and all were beautiful. I was shocked at the amount of flowers still blooming in October.

I'd go whenever works out for the rest of your trip!