As a rule, museums are open from 9 or 10am until 5 or 6pm. Others open later and close at 8 or 9pm. Closing day is most usually Monday or Tuesday, with a few exceptions. Some are even open 7 days a week, such as some of the major monuments which can even be visited as late as 11pm or midnight.
Opening times tend to be longer during high season, sometimes from April to October or from May to September, or simply in July and August.
Don’t forget too that on public holidays – in particular, 1 January, 1 May and 25 December – many museums and monuments are closed. It’s a good idea to check beforehand weekly closing days of cultural sites in Paris.