MD-11 Captain reported landing gear handle would not move to the up position after takeoff. The flight crew performed an air turn back and precautionary landing.

Narrative

After takeoff landing gear handle would not move to the up position. Ran the 'Gear handle will not move to the up position' checklist which has you push the handle release button and move the handle to the up position. The main landing gear retracted but the nose gear remained down. This led to the 'Gear primary or secondary light(s) illuminate with gear handle up' checklist which has you lower the gear and maintain speed. Gear lowered and was verified down and locked. Requested priority handling with ZZZ Approach and requested vectors. Then ran the 'Ground sensor failure' checklist as ground shift had not occurred. Received vectors to ILS [Runway] XXC; ran normal checklists and made an uneventful landing. Did not dump fuel or request equipment however Fire/Rescue was standing by. On landing rollout the nose gear seemed to settle or compress to a low position with an unusual vibration. Stopped on runway and had Fire/Rescue inspect the nose gear; they reported that the nose gear appeared normal. Cleared the runway and taxied to parking uneventfully.