What is the cheapest way to travel from Hamburg to Paris and back? I think flights are comparatively expensive, specially, as I know of no Ryanair hub around there. A slower way than flying is acceptable, but it should not take too long, at least not more than a day to travel.
Usually it is possible to get cheap fares for the train from Germany to neighbouring countries via the Sparpreis finder. If I'm not mistaken, it should be possible to get a ticket starting from €49. The cheap tickets tend to run out quite early, so you'll have to book them as soon as possible. The earliest date you can book them is usually 3 months before the date of travel.
Obviously taking the train will be rather long.
The main options would seem to be:
- Driving If you just travel on your own, petrol alone is a significant expense and you will want to avoid most of the French motorway network to save on tolls but it's perfectly doable in a day. That's assuming you have a car, obviously, if you need to procure one (buy/rent/import), you can forget about this solution. Cheaper variants would be hitchhiking (obviously a lot of uncertainty in that, it's not particularly difficult but there are no guarantees that you can make it all the way to Paris in a day) and ridesharing (“covoiturage” in French, “mitfahren” or “Farhgemeinschaft” in German). Also by road, bus travel is relatively cheap. Eurolines in particular is well-known for international links in Europe but there might be others.
- Train If you just run a search the most obvious route is going to be Hamburg-Cologne-Paris but it's likely to be expensive. You have to be a bit more creative, look for special offers, book well in advance, try to use local trains to avoid Thalys if necessary. Avoid the SNCF websites like the plague and go straight to bahn.de. One offer in particular could be interesting (and is perhaps even the cheapest solution of all except for hitchhiking): “Europaspezial” which can bring you to France for €39. You can search previous questions on this site for more info. Finally, night trains can also be affordable and could save you one night's accommodation (I believe there is a direct train between Hamburg and Paris).
- Plane Probably not the absolute cheapest way but even legacy carrier can have bearable fares, Rome2Rio suggests a ticket with Lufthansa starts at about €100. You have to factor in the cost of going to/from the airport, especially with budget airlines. Ryanair flies to Lübeck and Beauvais but not between them (and they are quite far from Hamburg and Paris, despite what they want you to believe). Don't forget that there are many other budget airlines in Europe (including Easyjet, Air Berlin and Germanwings) so it might be worth researching this a little more. For example, Germanwings apparently offers direct flights Hamburg-Paris for €33 starting in January.
All in all, you have many options slightly north of €100, which is not that expensive in historical perspective but obviously not extremely cheap either.
PS: You mentioned Hamburg in the title but Bremen in the text. Exact price and possibilities will not be exactly the same if you want to go from Bremen (and Lübeck, which Ryanair presents as “Hamburg” is on the opposite side of the city).