I know that the colonial powers of Europe met in Berlin to carve up the African continent, but why did they bother claiming Saharan lands? Why did French Sudan, Algeria, Italian Libya, and many other colonies jut out into the Sahara to cover as much land as possible? It seems more of a burden to enforce a claim over inhospitable land that appeared to have had little to no value at that time, so why did they still stake in a claim? Why didn't they just stick to the coastal areas and leave the peoples in the baren interior of the continent alone? The Arabian peninsula was mostly left alone besides the coast since they thought it was just useless desert, but why was the Sahara claimed?
Well this took place during the Scramble for Africa (1885-1910) when there was colonization of the African interior for the first time. Prior to this, European powers had just taken coastal areas and trading ports as opposed to the interior.
So the reason for the sudden colonization of the interior was because of improved navigation, cartography, steamboats and railways which allowed the Europeans to access the interior and moving away from the coast where they had previously relied on their ships for transport and supplies. In the grander scheme of things, the reason for the Scramble is more complicated, and basically the Europeans had developed these intense rivalries and colonization was about acquiring prestige and all about balance-of-power. If you had colonies, you were considered a "great power" and they were used as bargaining chips. There was no real practical reason behind colonization of a country like Mali for example other than securing access to the Niger river and connecting French Algeria with French colonies in sub-Saharan Africa on the map. There was some economic and strategic value in having control of the Saharan caravan routes, but this wasn't really taken into consideration.
So the Sahara is a desolate land that wouldn't have had little economic value or strategic use to France, but nonetheless France began sending expeditions in 1898-1990 beginning with the Foureau-Lamy mission (1898) from Algiers through the Sahara desert and to the Chad Basin, the Voulet–Chanoine Mission (also 1898) was sent from Senegal to meet them in the Chad Basin from the other direction and consolidate all the land in-between, and the Gentil Mission was sent from the Congo to Chad Basin (1899). The purpose of these missions were to sign alliances with the tribes and defeat the rebellious ones and create protectorates under French-rule and a "French West-Africa" with established borders on the map and a cohesive territory. The French did not need to "occupy" all their lands with soldiers, and they allowed the interior tribes to continue their way of life more or less.
The other reason for colonization of the interior was for rail-ways and trade/transport. The French for example wanted to build a Dakar–Djibouti railway from west to east across Africa. In order to do this they needed the land in between and access to the rivers Niger and the Nile. Meanwhile the British wanted a Cape Town-Cairo railway and they wanted to form a land connection from South Africa up to Egypt. This clash of interests led to the Fashoda Incident (1898) when both France and Britain argued over control of a tiny village in South Sudan and they almost went to war over it. This goes to show how intense the colonial rivalries were. After Fashoda, the French became especially aggressive in colonization and sought to take everything before the British could. This was typical during the Scramble for Africa.