Orange is a big player on this market, probably thanks to the fact that (as another user mentioned) Alcatel is one of the largest manufacturer (both historical french companies).

You can follow Jean-Luc Vuillemin [0] on Twitter for very interesting pictures of ships laying cables around the world.

One of the largest undersea cables plant is Alcatel in Calais, France (Dover straits). The factory is linked to the port by huge tunnels under the city. Unfortunately the Wikipedia page is only available in french but contains nice pictures[1]

[0] https://twitter.com/jlvuillemin [1]https://fr.m.wikipedia.org/wiki/Alcatel_Submarine_Networks