French organisations and businesses close on public holidays.
Although some shopping centres and grocers open for part of the day, the majority of shops do not.
Police stations and hospitals do not close.
When a public holiday falls on a Thursday or Tuesday, it is common practice to "make the bridge" (faire le pont) by taking off the Friday or Monday so creating a very long weekend. When this happens you may find businesses running on short staff or smaller family run business closed for the full period.
Museums and monuments in Paris are more likely to be closed on 1 January, 1 May and 25 December. Be sure to check beforehand.