Many public or similar bodies, as well as some companies, make the data they produce available through Open Data websites that allow for online downloading and/or consultation.
It is impossible to list all these portals that concern all sectors, but here are a few examples:

It's not difficult to find datasets because you only have to search Google and combine the query with the words "Open Data" to get many results. But there are also some major search engines that can also help:

 Open Data Inception which lists more than 2600 Open Data websites worldwide, including more than 400 in France

 Open Data Monitor, website funded by the European Union

 European Union Open Data website  

 French website for Open data