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https://www.google.com/maps/search/nice,+france+bike+shops/@43.6865746,7.2281189,13z/data=!3m1!4b1
Hit each one until you score a box.
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I dumpster-dived for cardboard, buy 2 rolls of tape and all's good. The shops in Nice are small mostly and they were out of boxes by the time I could be arsed to pack up my bike last year. I intend to tip off the shops in the area to hold onto a stock this year for 6-15th Sept, and say that they should expect beer or croissants in return for boxes : )
Nice airport sell boxes for 20E at the baggage services are, far right end of departures. Be warned, they're thin with no hand holds. Big though. ie, a PITA to move around but you can ride to the airport then box it up and go. Take your own tape or buy there. Book in advance ideally also, though I haven't in the 3 times I used them.
Get the train back - TGV to Lille, Eurostar to London. Takes about 8 hours.