I'm sure someone will find a quick and easy way for this achievement as they have for most of the other leader or culture specific ones.
For now I want to provide some pointers.
1. You do not
need to start
as a French
(faith). Though starting somewhere close to France, which usually makes you Catholic anyway, helps.
1a. So long as you have any Christian faith
you can convert to Catholicism through the faith menu. I recommend starting as a Catholic to save yourself the trouble.
1b. If you hold a county which has the French culture
[edit: possibly needs to be (de jure) part of the kingdom of France] you can move your capital there, though only once per character. After that you will get the option of converting to your (new) local culture in your decisions menu.
Beware: Don't do that unless you're close to finishing the other requirements or whatever else you had planned for your game. You will lose access to the innovations of your original culture which could result in an unwanted change in inheritance rules and other unpleasant stuff. And since you can only switch capitals once per lifetime you can't just go back afterwards.
Unconfirmed: You could possibly set your capital to a French county as one character but only convert to the local culture with your heir who should then have the option of changing their capital available again, which should in turn allow converting back to your original culture.
To change your capital you need to not
be at war. Select your desired county and click the crown icon.
2. Conquering the Kingdom of Thessalonika
from outside Byzantium can be a lengthy process. Unfortunately you cannot use a Holy War for Kingdom
against Byzantium (even if you meet the high requirements) as their faith is only considered "astray" by Catholicism. So either get lucky and have some claimants for relevant duchies visit your court or have your Patriarch fabricate claims on the individual counties which could also grant you a claim to an entire duchy.
After each war you have to wait 5 years for the truce to end.
3. Before you can attack the Byzantine Empire
with any chance of winning you will require a suitable army
. The easiest way I found to get ahold of that much power was through the Holy Roman Empire. If you start as a vassal to the HRE you can become Emperor yourself by either using the Meritocracy perk from the stewardship lifestyle to gain a claim, using that claim to create a faction against the Emperor and either getting your ultimatum accepted or by winning the ensueing war with your allies. The kidnapper perk from the intrigue lifestyle helps win wars quickly. As soon as the emperor is in your dungeon the war will be won.
Or you can slowly rise up through the ranks by first conquering land around your starting position, claiming kingdom titles and becoming eligible for the HRE elections yourself. After that it's as easy as having some of the electants like you more than the others. Alternatively you can try and get a hook on some of the electants and use that just before the emperor's death to force their vote. Unfortunately this is only good for 5 years and you can't always be sure when the emperor will die (unless you are responsible yourself
4. A good leader
I found to start as is Duchess Matilda di Lucca
in 1066. She is Catholic and as she's Italian this coice makes it easy to combine this achievement with
which requires the conquest of some of Greece anyway,
as well as her own achievement
: Start as a Catholic vassal to the Holy Roman Empire, usurp the HRE, conquer the Kingdom of Thessalonika and a French (culture) county, move your realm capital there, go to decisions menu and select Convert to local culture
This is my first solution, so any suggestions or additional pointers are welcome and will be added and credited to you once I find the time.