You are in Europe and you are a British 'self employed sole trader' therefore you are not liable for customs duty income tax etc (except in UK). The same laws that apply in Europe apply to you as they do in the UK. Not knowing what you are selling or doing I can't give you advice in detail, suffice to say that contract law in France is the same as in UK EXCEPT!!
In the UK, contract law requires that a contract be legal and that there be consideration (ie some reimbursement) in France its the same but you cannot offer free gifts to entice people to buy; each gift must have a nominal charge normally one euro. Equally, the operation of contracts within contract law requires an invitation to treat (your advert) an offer (your price or your ROM cost) and acceptance (the signature on the dotted line, the hand slap or whatever). In UK contract law it is the acceptance that is the contractual element, in France it is the offer (or devis) that is the contractual element. ie in France if you were a builder who offered to change a roof for 14000 euros and the customer signed, you cannot then go in and say ah well actually I cocked up and only measured one side of the roof instead of both sides, you have to do the job for the price!! Needless to say any arguments normally get sorted in court and French courts can take about 4 times longer than in UK.
Still a market cannot be simpler. Make sure that you have any appropriate electricity supplies and that the basic facilities are available ie toilets food etc. If it is a market in Paris in the winter make sure that you have heating and warm clothing and good flooring (take cardboard to stand on if it is the bare concrete).
I would advise you to use cash where you can since credit cards cost money. However, since you probably won't have a French bank account and the French are quite advanced in the use of credit/debit cards you might need to hire a UK card terminal but I am not too sure of the ins and outs of those. If you are going to accept cash only, then make sure you have a good secure stash somewhere, sadly many of the new migrants (and old) are not adverse to helping themselves esp in Paris.
You said that you had been invited I assume that means that you will have a sponsor/friend or whatever, ask them if you are invited as part of an 'Association' there are different rules for those which tend you give you more legal protection.
If you are going to turn wood and give demonstrations then make sure you have liability insurance. It is now mandatory to have it in France which is why I am stopping at the end of this year, because before my own household liability insurance covered it from Jan 2016 it doesn't.
There are but a few elements, in the main there is no great difference between a UK market and a French one except the language and anyway it is trendy to speak French with a British accent at the moment!!
send me a pm if you want to know more (I worked for 6 years in Paris) we'll swap phone numbers and you can ask your questions then.
Pierre