The Paris flea market can be said to be no less safe than Paris or than any other big city in general.
Getting to the market from metro Porte de Clignancourt can be a bit tricky, as you need to walk 10 minutes and get yourself past the knock-off stands and – sometimes – the pickpockets.
Once you find yourself inside the flea market proper, apply the standard, common-sense rules: beware of pickpockets, avoid wearing expensive jewelry, and do not wave your money conspicuously.
Inside the Paris flea market you will find one ATM cash machine, and two (high-commission) cambio windows.
The Paris flea market does not have it’s own taxi stand. To obtain a taxi, ask the tourist information center, or ask your tour guide, to call for one.
After your visit, the 85 bus takes you from the flea market all the way back to Châtelet in downtown Paris and to Luxembourg gardens at the top of the Latin Quarter. Bus 85 runs every day, including Sundays. You can also take the 4 or the 13 metro line, each located some 10 minutes’ walk away from the market.