The formal dedication of France's new military base in the United Arab Emirates has been attacked by some in the Arab world as a revival of colonialism. In fact, of course, France is just gaining a small military support base in the Gulf, its first. While certainly the Gulf depends on Western naval power for its defense, that task is primarily provided by the US, which has a far larger presence than France is going to have. The French foothold is nothing compared to the US Fifth Fleet presence in Bahrain, the heavy US presence in Kuwait, or the big and growing US airbase at al-‘Udayd in Qatar.
The fact that France is a former colonial power in the region may spark some sensitivities, but France never had a presence in the Gulf, and its forward presence in the region is still much heavier in Djibouti than it will be in Abu Dhabi. This clearly is not a return to the days of colonialism, when France could try to hold on to its base at Bizerte against the will of the Tunisian government, or when the British resisted withdrawal from the Canal Zone. There are no more "old style" colonial presences in the region (with the notable exception of the British Sovereign Bases on Cyprus, but Cyprus is a special case). These base facilities represent a mutual interest of the host country and the basing country, and are always subject to the continued consent of the host country. When Saudi Arabia wanted US forces out of the Prince Sultan Air Base, they left. Some US facilities in the region are not publicized, because of host sensitivities, but none are present without the consent of the host country.
The real news here, I think, is that France is assertively projecting its presence into the Gulf region, refusing to see the Gulf as an American, and formerly a British, lake. The French military industry is dependent on foreign sales to survive (foreign sales help finance production for the French military), and the UAE is one of its biggest customers, perhaps the biggest.