Yes, France would technically have the mean to conduct such an en masse deportation. But to paraphrase a popular movie, "You were so preoccupied with whether you could, you didn't consider if you should".
Firstly, sending settlers to colonies is an primarily seen in the New World. Outside of there, sending settlers to colonies is not done, with the sole exceptiona of Australia and New Zealand. Even within the Americas, it wasn't done because the empires wanted to change the demographics of the colonies. The main goal of a colonial empire is to reap money from the colonies and to secure resources. Settling wasn't part of the equation. To achieve these goals, labour is needed. Most empires were willing to let the new world natives be the backbone of the colonial economy... until disease and war decimated them. So the colonialists had to find people to emigrate en masse to the colonies to fill the gap. In North America, this lead to many European settlers coming to find jobs. In Africa and Asia, there existed a native population, so there was no need for anyone to settle en masse. So I don't see why would do such actions in the first place.
But I shall oblige with your OP. Since you mentioned 1945, I'm going to assume the plot to deport the natives occurs in the period immediately after WW2 to about the mid 50s.
Two ways this could play out, pre of post NATO.
Pre-NATO
Somewhere in the mid to late 40s, France plots to deport the population of Djibouti. There's just one problem with deporting the Djiboutians to the neighbouring lands; one of the neighbours would be British Somaliland. British colonial authorities there would be among the first to know of France's plans. The British government would then be informed. For several reasons, the Brits would formulate their response. The response being: a brief, undeclared war to kick France out of Djibouti. I know this sounds like ASB, but bear with me. Reasons why the UK would intervene:
1. Simple humanitarianism- there would be those concerned that France is conducting a campaign of demographic replacement of an African population
2. The colonial authorities do not want to deal with a refugee crisis.
3. France is militarily weak- France had yet to recover from getting clobbered by Germany. The empire at this point is only really held together by the French colonial troops. Given France is deporting a native population, I'd imagine there would be a few mutinies among the colonial army and the local law enforcement, furthering weakening the already weak French control.
4. Monopolizing British influence along the African coast of the Red Sea- This reason is the most important of all. In the aftermath of WW2, the UK had a lot of influence on the African coast of the red Sea and Horn of Africa. There's the aforementioned British Somaliland, British occupied Eritrea, and Anglo-Egyptian Sudan where there was direct influence. Egypt, with a large Red sea coastline and the Suez Canal, had a pro-British king. So even though Egypt was independent, the UK still influence there. The only other competitor on the African continent was France. So kicking them out would expand British control along this major body of water.
So Britain would use France deportations as casus belli and start an undeclared war. This war is likely to end within about a week with the UK taking full control over Djibouti. In addition to the weak ground forces, another reason this war would be over so quickly is the massive naval difference. After WW2, France simply didn't have a navy, and the UK, even though bankrupt, was still known for its naval prowess. The UK could easily blockade Djibouti and prevent any French reinforcements and supplies, however they might arrive, from entering.
The UK would then incorporate Djibouti into british somaliland. As with the rest of British somaliland, it becomes part of Somalia
Post-NATO
Obviously the UK can't just attack a NATO member, so it would have to do something else. And that something else involves Nasser. Given Nasser would opposed to France in Djibouti and his open intent to nationalize the Suez, the Brits go him with a proposition, they would back him in kicking out France from the Suez Company and turn the venture into an Anglo-Egyptian run company. The two would then issue an ultimatum: France is to stop the deportations and accept all the refugees returning or lose access to the canal. The US, having an anti-colonialist worldview, would back the UK and Egypt. The USSR being anti-imperialist would also back the two, but mainly Egypt. Faced with such pressure, obliges.
Aftermath
French-UK relations obviously deteriote. This saga would be used among the many justifications France would use in threatening to leave NATO. It would set relations back a few years and won't be until the 70s when they get fully repaired.
Interestingly, this may cause the Suez Canal crisis to not happen. France, because of its bad relations of the UK and/or no longer having a stake in the Suez company, do not want to participate in any military action with the UK. Without France, Israel might call its quits. All alone, the UK negotiates with Nasser for a buy-out instead of being kicked out.
