Owners usually start with the wrong battle: trying to rank for "gîte in Dordogne". That query belongs to platforms and directories that outspend you, and it is not the one that fills a calendar.
The battle you always win: your own name
When someone recommends you, the person types the name of your gîte. Without a site, that search lands on your listing and you pay commission on a booking you brought in yourself. With a site carrying your name in its title and domain, it lands on you. Nobody else is called what your gîte is called.
The Google business profile
Free, and often more visible than a website for a local search. Three things matter: photos, plenty and current; reviews, asked for in person at check-out; and a link to your site rather than to your listing.
Long queries nobody competes for
You will not win "gîte in Dordogne". You can win "heated pool gîte for 8 near Sarlat, dogs allowed". A page that actually says what is there — pool temperature, drive times, number of bedrooms, pets, step-free access — ranks for dozens of these with no SEO effort at all.
What does not work
Buying links, stuffing keywords, publishing machine-written articles about the ten prettiest villages nearby. One honest, detailed page about your place beats twenty generic articles.