Hi, and welcome to the forum.

Unless you're real fluent in French and somewhat familiar with France, I'd look for a shipper and storage company in the London area, and have your stuff shipped to you once you've found an apartment in Versailles.

Though I don't have any personal experience on the London to Versailles run, I have found that French rules and practices for things such as moving and storage can sometimes be a bit "surprising." At least if you work with a British shipper and storage facility, there shouldn't be too many surprises, and if something happens, you can deal by phone in your own language.

A friend of mine living here in France moved back to the UK, and the move was paid by the company her husband had worked for. They specifically told her that they would engage a British or German removal company, simply because they "had bad experiences" with the French companies they had used in the past. Now, it's possible the bad experiences were the result of misunderstandings, but it's generally easier to go with the language and culture you know, at least when first moving to another country.

Just my take, anyhow.
Cheers,
Bev