Miss Markle who has relocated from her home in Toronto, Canada, will also be taking British citizenship to become a dual national before May, a process that usually takes years.
It is not clear whether the actress will retain her US citizenship and become a dual national in the future.
French President Emmanuel Macron is expected to raise the issue when he visits Theresa May for talks early in the new year.
But sources at the Brexit department today said ministers would make clear to their counterparts the British taxpayer would not pay for infrastructure in France.
The actress' divorced parents Thomas Markle and Doria Ragland will both be there but it's not known if her father will walk her down the aisle.
It can be fun, terrible, exciting, hard — the adjectives used to describe it are endless.
Paris believes Britain should also share its additional costs under the Le Touquet treaty - a bilateral agreement between the UK and France on the Channel ports (including the Channel Tunnel, pictured).
But Mr Duncan Smith said: 'There is no logical or legal reason why Britain should pay anything towards this.
The couple's first public engagement will be on Friday at the National Justice Museum in Nottingham.
Britain will tell France it is 'out of the question' for the Government to plough cash into new customs controls across the Channel after Brexit.