I am curious whether it's just my brain that doesn't work right
You're describing your travel experience to someone... which of these sentences would you SAY? As in, speaking, not as in writing an email/etc -- you're at the office or somewhere talking to somebody. Assume that you actually have the experience of travelling to France and Spain at some point in your life, and someone's asking you about what countries you have the experience of travelling to or plan to travel to.
(oh, and assume appropriate abbreviation, ie, "I've" instead of "I have", if that helps.)
[Poll #1413618]
And a better question: does it change if you are writing a report or article rather than just speaking?
(oh, and assume appropriate abbreviation, ie, "I've" instead of "I have", if that helps.)
[Poll #1413618]
And a better question: does it change if you are writing a report or article rather than just speaking?

no subject
no subject
If someone comes up to me to talk to me on the subway and is practicing their English and says "Where are you from? Oh, Seattle? I have visited Seattle once! The weather was very rainy."
...I understand what they're saying, but my immediate thought is "You are speaking very good Textbook English, sir, and my guess is that you did not spend a LONG time in the USA."
Because I think that speaking naturally, most of us would say "Oh, Seattle! I've been there once! It rained a lot!"
no subject
no subject
Have you ever been to Tokyo?
--I visited once last summer.
--I lived there for three years.
--I've been there a couple of times.
I think it's perfectly natural to use visit in its context, although it's a bit specific to ask if someone has ever visited a place...
A: I used to live in Tokyo when I was young.
B: Have you been back to visit?
no subject
I've been to France.
I visited France.
I've seen France.
I've taken a trip to France.
all have subtly different meanings and they can all be useful in spoken English.
Somehow "I've / I have visited France" seems less appropriate for spoken English than without the "have." I think it might have something to do with when I would use "visit." Specifically, I think I would be most likely to use it when telling a story. I forget the various tenses, but I have foo isn't the past tense you usually use for telling a story.
no subject
no subject
no subject
But either way, "I have [verbed] before" or "I [verbed] once." If you say "I have [verbed] once" it emphasizes "exactly once."
no subject
no subject