I can only think of a few,
USA: Mickey Mouse
Japan: Godzilla
UK: Sherlock Holmes
France: Hunchback of Notre Dame
Most of the ones I immediately think of for other countries are the product of American or other foreign creators. Can we compile a list of 200+ such fictional characters?
Spain: Don Juan or Don Quijote, I leave that to others to decide 
Switzerland: Heidi
Belgium: Tintin (or perhaps Hercule Poirot. I would vote for Tintin).
Germany: the Struwwelpeter
I disagree on France and say: Fantômas instead
Agatha Christie was British if I’m not mistaken.
I oversaw the “domestically created”, sorry. So Tintin was better indeed.
Not a bad choice, but I’d argue that Dr. Faust(us) is more iconic and better known internationally.
ETA: or arguably Max und Moritz.
That is a fair argument.
ETA: Max und Moritz were my second option.
Italy: Pinocchio
That’s a good one! I almost wonder if Disney ever comprised a similar list for potential appropriations.
Another option for France: Asterix and Obelix.
Mexico: El Santo
England: Sherlock Holmes.
ETA: alternatively, James Bond.
USA: Ward and June Cleaver.
Finland: Moomins
Canada: Bob and Doug MacKenzie, eh?
Not Papa Smurf?
Powers &8^]
Netherlands: The Flodders.
For Britain, I’d go further back and call their iconic character either Robin Hood or King Arthur.
Or Superman
Czech/Bohemian/Austrian: Gregor Samsa.
Swiss: Willhelm Tell
I was going to propose the Golem, but I like yours better.