|Quoting Schweigend (Reply 2):|
Visiting Paris -- Ahh, that could be done easily once you've gotten to Scandanavia by buying a separate airline ticket for a discount price or by taking a nice train. Also you could rent a car (from CPH)
Travelling on the train from Sweden to Paris takes ages. Not sure if the OP is willing to do so.
Oneway car rental within Europe, dropping the car off in a different country comes with a hefty (!) oneway fee.
A quick check on Hertz (others might differ a bit) has a oneway fee of around 1300 € / 1700 USD for a oneway Stockholm to Paris (plus the car itself).
While not in concern here, there are restrictions on where you may drive a rental car to (like entering certain countries (sometimes varying by model), taking car onto a ferry (--> driving to U.K. ; not sure about using the Shuttle through Eurotunnel though ). Always check with agency !
Remember that there is a mandatory security check involved when entering KEF (for connections or for arrivals).
As Andaman poited out already, then London is a no-no as the U.K. and Rep. of Ireland are not member of Schengen zone.
Would only make sense if you include a stop-over at Paris (on the outbound leg); if not possible or economical, than routing via CDG is a detour.
Same goes for LH via FRA.
Booking an open-jaw with any airline forking between ARN and CDG could be an option (on any airline). Organize any intra-european travel seperately then.
How much time do you want to allocate ?
Paris itself (including daytrips into surrounding areas) warrant a vacation in itself.
The same would be true for London, but again: This is not Schengen zone !
Travel between Paris and London best is done on Eurostar trains going center to center, whereas airports (CDG and LHR) are located away from city centers and their relative congestion only adds to total travel time. The train will be faster.
With such a broad question, you will get a ton (!) of suggstions, even when restricting yourself to cities that (more or less) lie enroute (give or take some deviation from a dirct path) a surface trip Stockholm to Paris.
Suggestions would include (but definately are not limited to) Copenhagen, Hamburg, Amsterdam, Brussels.
A few more potential highlights are located off track (but everybody will have his/her own favourites):
Berlin, Krakow, Prague, Budapest, Vienna, Zürich, Florence, Rome, Barcelona, Lisbon - to name but a few (all within Schengen zone). Many more attractive landscapes to add ...
So, I recommend that you frist make up your mind on how much weeks you will be able to allocate for this whole trip.
Already those 3 countries in Scandinavia will take up some time ...
Do you intend also to head north across the Artic Circle in order to experience Midnight sun ? This experience is highly recommended. Depending on exact timing of your vacation (relative to 21-JUNE) you might decide on the excat place to head to.
Tromsoe in Norway is a good place.
The North Cape is said to be very touristy meanwhile.
A once-in-a-Lifetime experience could be to spend a night in the northernmost Full-service hotel (as they advertise themself), the Radisson Blu Polar in Longyearbyen on the island of Spitsbergen, about 600 miles north of the North Cape. Flights (in summer) are a few per day from OSL (Olso-Gardermoen) and TOS (Tromsoe) on SK and (maybe also) DY.
Just a few thoughts ...
Carpe diem ! Life is too short to waste your time ! Keep in mind, that today is the first day of the rest of your life !