Both forms are correct, you could present yourself as an "Ingénieur en Informatique" or an "Ingénieur Informaticien". There’re multiple ways of saying it. But the level of precision you want here is relevant.

IMHO "Computer Engineer" could be translated "Ingénieur Informaticien", whereas "Computer Science Engineer" could be translated as "Ingénieur en technologies de l’information".

Ingénieur Informaticien is the most understandable way to phrase it specially when you’re talking to non-IT related persons.

I have graduated what is equivalent to a Master Degree in Computer Science Engineering and this is the title used on the Diploma :

Ingénieur en Informatique et Réseaux

My present job’s title is :

Ingénieur en Technologies de l’Information

Ingénieur TI / Ingénieur IT (anglicism)

It’s also possible de find people with the following title :

Ingénieur en Nouvelles Technologies de l’Information et de la
Communication

Ingénieur NTIC

I don’t perceive a nuance between the two French terms and I see none as a correct translation of computer engineer. IMHO computer engineering has hardware connotations that I don’t see in terms derived from informatique (BTW, computer scientist or software engineer are not good matches for the French terms either which cover IMHO more).

I don’t see a good term which would closely correspond to computer engineer. Terms I can think of either cover only part of the aspect (ingénieur réseau for instance) or at the same time cover more and are missing aspects (like informaticien or électronicien).

I fear that you’ll either have to resort to term which is not a perfect one, or a periphrases if you want to stay close to the meaning.

Please keep in mind that ingénieur, especially when presenting oneself on a CV, is usually taken as designating the holder of the official diploma (ingénieur diplômé). I would interpret Ingénieur en informatique on a CV as short for Ingénieur (diplômé) (avec une spécialisation) en informatique, and Ingénieur informaticien as short for Ingénieur (diplômé,) (travaillant comme) informaticien.

In short, I would expect a non-French ingénieur en informatique to actually have a degree in computer science, preferably Masters-level, while I’d not expect it of an ingénieur informaticien.

Source 1: I’d like to check what’s actually written on mine, but I don’t have it at hand!

Source 2: Comment ça marche

Are both correct ?

Yes.

When writing an official form+document, which one should I use?

It depends. If you apply to a computer services company (Fr : Entreprise de Services Numériques (ESN) , formerly Société de Services en Ingénierie Informatique (SSII)), a generic label is Ingénieur Etudes & Développement.
However, keep in mind that we are talking about a “generic label” and not an official title.
The only title you will be able to find in France is Ingénieur diplômé.

Engineering schools get their accreditation from the CTI (Commission des Titres d’Ingénieur). If you have this title, use it. Otherwise, I recommend Ingénieur en Informatique for the reason below if you want to stay generic.

Are there any difference between those two?

Litteraly speaking, no. Except they suggest a different personality.
Ingénieur informaticien is a bit 80s so you would prefer the other one.
Any french software engineer eventually hears about this video : Michel l’ingénieur informaticien sur YouTube. There are other humorists (Les Inconnus, for instance) that made fun of nerdy software guys at that time, so you normally want to avoid that label 🙂

I personally don’t like new titles as “Ingénieur NTIC, Ingénieur IT, etc” as you don’t know what it means (network ? software ? admin ? coffee ?).
When specicifying “Ingénieur” in your resume, you suppose that you have a Master degree in computer science. (Traditional engineering schools last 5 years in France).
I prefer to specify the area I mainly work on. I use “Ingénieur en Développement”, as I work as a developer and have a master degree (and the title /bling /bling). You can use “Ingénieur X” according to your activity.