Zone Internationale (International Zone) / Démilitarisée (Demilitarized)

It refers to the Part III, Section 1, Article 36 and Section 2, Article 37 of the treaty.

ARTICLE 36.

Subject to the provisions of the present Treaty, the High Contracting Parties agree that the rights and title of the Turkish Government over Constantinople shall not be affected, and that the said Government and His Majesty the Sultan shall be entitled to reside there and to maintain there the capital of the Turkish State.Nevertheless, in the event of Turkey failing to observe faithfully the provisions of the present Treaty, or of any treaties or conventions supplementary thereto, particularly as regards the protection of the rights of racial, religious or linguistic minorities, the Allied Powers expressly reserve the right to modify the above provisions, and Turkey hereby agrees to accept any dispositions which may be taken in this connection.

ARTICLE 37.

The navigation of the Straits, including the Dardanelles, the Sea of Marmora and the Bosphorus, shall in future be open, both in peace and war, to every vessel of commerce or of war and to military and commercial aircraft, without distinction of flag.

These waters shall not be subject to blockade, nor shall any belligerent right be exercised nor any act of hostility be committed within them, unless in pursuance of a decision of the Council of the League of Nations.

It also refers to Chapter III, Article 178 / 3

ARTICLE 178.(3) The territories of the zone and the islands of Lemnos, Imbros, Samothrace, Tenedos, and Mitylene shall not be used for military purposes, except by the three Allied Powers referred to above, acting in concert. This provision does not exclude the employment in the said zone and islands of forces of Greek and Turkish gendarmerie, who will be under the Inter-Allied command of the forces of occupation, in accordance with the provisions of Article 161, nor the maintenance of a garrison of Greek troops in the island of Mitylene, nor the presence of the Sultan's bodyguard referred to in Article 152.

Turkey under the Treaty of Sevres were almost forbidded to have an army. It would have gendarme as a police force but militarily speaking, she can't have an army and certainly can't deploy it to Istanbul/Bosphorus.

I said almost because It could have an army size of 50.700 (if memory is correct). But 50.000 means nothing and army was forbidded to posses any heavy weapons.

Additionally, straits are to be militarily controlled by others (French, Greece etc.), not Turkey, so in a sense, it's demilitarized.

Zones D'influence (Sphere of Influence)

This basically means Sphere of Influence, in short it means a state/part of state that is culturally or politically influenced by an imperialist nation. It doesn't mean they have control over these zones but It could mean something like France coming in and saying "we need a few more French schools".