A low pressure system will be sitting over England Wednesday and Thursday. This will bring periods of showers to Le Mans, which may affect the practice and qualifying sessions on both days. The low pressure will start to push east into the North Sea on Friday, but a trough trailing behind it will still be located over Northern France, so periods of showers will continue. Temperatures will be cool under the low pressure system, with highs only in the mid 60s F (upper teens C). The total amount of rain expected Wednesday through Friday is between a quarter to half an inch (6 to 13 mm). Let me clarify that I don't expect this rain to be a constant, all day rain. I expect that it will be more on/off showers, most of which will be light.
There's a chance of some showers lingering into Saturday morning, but by the afternoon, the rain should be gone and the sun should start to peek through. With high pressure building over the region, I expect that the entire race will be dry from start to finish. Sunday looks like a pretty nice day, with a mix of clouds and sun and a high temperature near 70 F (21 C).
We don't have radar available for France as we normally do, but I recommend Weather Underground if you want to check the radar or current observations.