Hello,
Just some observations.
In American English we might say: I have to make a trip to the grocery store. Do you need anything?
Make a trip or take a trip just means "to go" in this context.
A tour connotes seeing the sights, learning something, with a guide or self-guided. It can be touristic or work-related as in "Today I have to take all the new employees on a tour of the factory."
An excursion can also mean a detour or deviation, as in "During the course of the lecture, the professor made a needless excursion into his personal life." (He stopped talking about the main topic and started to talk about something else.)
To answer your specific question, they are not specifically interchangeable, since each word has a connotation or nuance. Here's an example of how I would understand each word. If you say...
1) I am going on a trip to France. (I would think you'll be in France for several days or more on vacation or business.
2) I am taking an excursion to France. (I would think you were actually in another country somewhere close to France and just going over for a day trip or a short visit)
3) I am taking a tour/touring France.(I would think there is a specific itinerary with or without a guide.)
To visit a single sight, such as a museum or castle, "excursion" or "tour" would normally be used. "Trip would suggest that the museum or castle is farther away.
Hope this helps a bit!
Best,
Martha