How do I change the link structure of my moved WP ?

Greetings,

So I've been working on a new website that was located in a subfolder : http://www.aaaaa.com/new-site to replace an old site located here : mysite.com

Once the new website was done, I asked my server guy to make a change in Apache so that the "mysite.com" domain name points to the new site's folder on the FTP (let's say it's var/www/aaaaa/newsite).

So now, I can access the new site when I type "mysite.com", which is good.

However, all the link structure is still based on the old links... Aka when I click on the contact page, the link is not "mysite.com/contact" but "aaaaa.com/newsite/contact", which is a problem.

How can I change that so that all the link structure is "mysite.com/page" and not "aaaa.com/newsite/page" ?

I suppose it's .htaccess related but I don't want to try crazy stuff since the website is in production.

I also did not touch the "Wordpress Adress" and "Site Adress" in WP Settings to avoid causing trouble.

What's the best, quickest, simplest way to proceed ?

Thanks A LOT in advance,

DJ