I will note from the outset that journal editors might require things from you that go beyond what is legally necessary. A typical case is that they will require one to obtain permission before reusing a figure from another article/journal/author (even though in the vast majority of cases no such permission would be needed). The legal answer might allow you to push back on the editor’s demands, but they still have the last word.
There are two kinds of intellectual property to consider. Unless otherwise noted, this answer is valid for france and united-states.
Trademark is almost certainly not an issue
Trademark is a right to branding. A trademark holder can prevent others from using certain elements to promote their own products. The elements need not be complex, they just need to be recognizable by the public as related to the brand in question.
For instance, "Tesla" is the name of an 19th century Serbian-American inventor known among other things for discoveries related to radio transmission. You would probably be able to market a radio transmitter under a "Tesla" brand (assuming there are no existing trademarks, which I have not checked). If you try the same thing with electrical vehicles, you will get sued.
For a research paper, as long as you do not imply that Visa or MasterCard support your research or its results in any way, that should not be an issue.
I assume, but cannot guarantee, that the above applies to most Western jurisdictions.
Copyright
Copyright is a protection or creative elements. Whoever authors a creative work can forbid others from distributing it under certain conditions.
Are the Visa and MasterCard logos copyrighted?
The first question is whether the elements at hand are protected under copyright. In the case of the Visa and MasterCard logos, this might depend on the jurisdiction. The criterion for "creativity" varies a lot.
Some jurisdiction have adopted (some version of) the sweat of the brow doctrine, according to which work suffices to produce a "creative element" with copyright protection. The typical example are databases of facts where each individual entry is unoriginal but the collection might take some time to collect, curate and maintain (such as a phone book).
In the united-states, the Supreme Court rejected the sweat of the brow doctrine in 1991. Accordingly, a work needs to reach the threshold of originality.
Determining whether the threshold is met for a given work is done on a case-by-case basis at trial. However, it seems very likely that both logos are not protected by copyright in the United States. The Visa logo is a simple font with no significant creative elements; the MasterCard logo contains two overlapping circles.
I note that Wikimedia Commons hosts both logos on their website and claims they are public-domain under that rationale (Visa, MasterCard). Wikimedia Commons usually follows copyright fairly closely, and they are a high-profile website hence a prime target for takedown requests by IP lawyers at Visa or MasterCard, so that is weak evidence that their claim is correct. But there is always the possibility that Visa / MasterCard just have not decided to sue yet.
In france, the statute makes no explicit reference any threshold of originality: (article L-112-1 of the code of intellectual property)
Les dispositions du présent code protègent les droits des auteurs sur toutes les oeuvres de l'esprit, quels qu'en soient le genre, la forme d'expression, le mérite ou la destination.
The present code [containing all copyright statutes] protect copyrights for any works of mind, whatever their style, form of expression, artistic worth, or intended use.
However, various court cases have tended to require "works of mind" to exhibit some amount of intellectual originality. For instance, Civ. 1ère 22 janv. 2009, n°08-11404 held that a perfume cannot be copyrighted because
la fragrance d'un parfum, qui procède de la simple mise en oeuvre d'un savoir-faire, ne constitue pas la création d'une forme d'expression pouvant bénéficier de la protection des oeuvres de l'esprit par le droit d'auteur
the smell of a perfume comes from the simple application of a know-how and does not constitute the creation of a form of expression subject to the protection of works of mind by copyright
After a fifteen-minute look at various cases, I still do not have any strong idea of whether the Visa or MasterCard logo would be copyrighted in France. Let’s assume for the sake of the argument that they are.
"Fair use"
Even copyrighted works can be used without the copyright holder’s agreement under certain exceptions. Here again, any precise answer is jurisdiction-specific.
"Fair use" is a US-specific doctrine, resulting from a string of court cases eventually codified into law (Wikipedia has a decent history). It is a rather general doctrine (any use case can be analyzed under the four balancing factors) and results can be hard to predict. I believe research articles usually fall on the right side, but because the logos under discussion are not under copyright in the US (see above), I will not attempt to make any in-depth analysis.
Pedantic note: it is sloppy wording to use the term "fair use" for similar clauses in other jurisdictions. "Fair use" is a US doctrine.
In france, the corresponding doctrine is given by a rather strict but precise statute at article L122-5 of the code of intellectual property:
Lorsque l'oeuvre a été divulguée, l'auteur ne peut interdire :
(...)
3° Sous réserve que soient indiqués clairement le nom de l'auteur et la source :
a) Les analyses et courtes citations justifiées par le caractère critique, polémique, pédagogique, scientifique ou d'information de l'oeuvre à laquelle elles sont incorporées ;
When the work has been published, the author cannot forbid:
(...)
3° As long as the name of the author and the source are clearly mentioned:
a) Analysis and short citations justified by the inclusion in a work with an aim of criticism, debate, pedagogy, science or information
A research article is the typical case of a "work of science" (science means here "scholarly research", not STEM). I have little doubt that it would be a covered use, especially if the paper discusses the reason behind the choice of those logos (easily recognizable by test subjects? simple shapes? etc.).
