It’s not a perfect replacement, but searching OpenStreetMap via https://overpass-turbo.eu/ with a query like
[out:json][timeout:25];
(
nwr["diet:vegan"~"yes|only"]({{bbox}});
nwr["cuisine"~"vegan"]({{bbox}});
);
out geom;
can be useful and is often more up-to-date with respect to restaurants that actually still exist.
An example: https://overpass-turbo.eu/s/2shI


So I will say as a contributor to OSM that your coverage is going to vary unbelievably vastly depending on where you are. There are many areas in the US, for instance (in fact, I’d argue most), where HappyCow has an active community but where OSM will be functionally useless and where you’ll have to bootstrap it yourself. Moreover, OSM even given an “ideal” level of maintenance has extremely poor granularity, very minimal standards for what constitutes a restaurant serving a dietary option, poor accessibility (having to issue a JSON query or use something like JOSM, the latter of which I would recommend as easier than Overpass; OpenVegeMap is dead IIRC), no inherent guardrails against outdated information that HappyCow lacks, no community of vegans maintaining it in most places, no reviews, and crucially no real way to express nuance via text (there’s a “note” param, but nobody in their right mind is regularly using it to explain the intricacies of a restaurant’s vegan options; that isn’t why it exists.)
Your example is in Paris, which is – I cannot emphasize enough – wildly unrepresentative of the map’s progress in most places. At least in the US, the average person is entirely better-served by HappyCow than OSM for this specific problem. Picking out Paris specifically is near-best-case for OSM.
I say all this recognizing that HappyCow for me has always also been a noticeably flawed experience.
Edit: As an example even for this near-best-case for OSM, here’s Mannie’s listing on HappyCow. It has three contemporary reviews, the contact, hours, and location info OSM has (OSM even in such a complete area funnily lacks the
website:menuparam, which the website definitely has; nice for convenience), images of the vegan dishes, an explanation of the veg options, and is overall just a much better, more thorough experience.The OSM item tells me vaguely that vegan option(s) exist(s); HappyCow tells me that they’re clearly labeled (massive), that there are multiple of them and what they are, what a vegan thinks of the quality, that there are gluten-free options (I don’t need this, but OSM allows it, yet it’s not there), and what the meals physically look like.
Edit 2: Accidentally duped my comment.
My post may well be tainted by my growing frustration with HappyCow growing increasingly out of date in my region. I frequently find restaurants listed that have long since closed and new restaurants not listed at all. But criticism in my workaround and its deficiencies has been wholeheartedly acknowledged and appreciated.
Though HappyCow is closed-source and proprietary, it’s like OSM in that it relies on user reports. Have you submitted new restaurants and reported closed ones?