I assume you checked with the seller that the fruits being sold do belong to a non-Jew (i.e., they are not just reselling Jewish produce) - see towards the end as this is not obvious. And of course you know this only applies during a shmita year
My reference book on shmita issues is R Yosef Tzvi Rimon's Shemita (full intro available here). Also exists in Hebrew.
He explains the point 3 from user15503's answer in great detail (pp. 144-149 and 372-376). In a nutshell
- There is a dispute whether shemita produce becomes ownerless through an active declaration of its owner or automatically ("a dispensation of the King") - the Bet Yosef argues for the first, the Mabit for the second
- According to the Bet Yosef, if a gentile doesn't declare his produce ownerless, it is not ownerless and the produce is subject to terumot and maasrot. This view is accepted bt the Pe'at ha-Shulchan, R Kook, R Shmuel Zalman Auerbach, R Pesach Frank, R Ovadia Yosef
- According to the Mabit, produce growing during a shmita year is automatically ownerless and thus even the produce of a gentile is ownerless and therefore exempt from terumot and maasrot
R Rimon writes that the accepted practice in Israel is that the produce of a gentile does not have shemita sanctity in accordance with the Bet Yosef, but in Bnei Brak many follow the view of the Chazon Ish who rules according to the Mabit.
However R Rimon has the following to say on buying fruits and vegetables from gentiles during shmita years, in practice
Despite all the above discussion, buying gentile produce is still not
a simple matter. Sometimes, and especially during the shemita year,
Jewish farmers sell their produce to Arabs in order to market it. Due
to security concerns, even careful supervision cannot always trace the
course of the produce, and it is often difficult to determine if it
was really grown by a gentile or sold to him by a Jewish farmer.
Moreover, significant areas of land in Eretz Yisrael do not actually
belong to the gentiles working them, but rather the lands have been
illegally taken over by these gentiles from Jews. In such cases, the
land is not regarded as the land of a gentile, and the vegetables
growing there are subject to the prohibition of sefichin (Responsa
Maharam ben Baruch, no. 536; Torat ha-Aretz, vol. II, section 3).
most serious problem with buying gentile produce, however, lies in the
fact that it strengthens the gentile hold on the land in Eretz
Yisrael. Even if from a strict halachic perspective this does not fall
under the prohibition of lo techonem, not granting gentiles a portion
in the land (an assumption which is not at all clear), the fundamental
problem underlying this prohibition certainly exists. [...] Without a
doubt, buying produce from gentiles undermines the idea behind the
prohibition of lo techonem.
Finally you should note that R Rimon writes at length (p. 499ff) that one should make an effort to buy from Jews whenever possible and when the price difference is not too significant
On the other hand, giving preference to imported produce is liable to
cause Israeli farmers heavy economic losses, bring about the collapse
of many branches of agriculture, and lead to serious set-backs in the
process of raising the standards of shemita observance. The larger the
community interested in purchasing shemita produce the easier it will
be to employ the superior methods of dealing with the halachic
difficulties posed by shemita, such as Otzar Bet Din or hothouses and
container produce, or to improve the heter mechira so that it will be
executed in the most halachically preferred manner. [...]
Tosafot's fundamental approach is clear: there is no obligation to buy
from a Jew over a gentile when doing so would cause a financial loss.
According to the Tosafot in Bava Kama (114a), this applies to any
loss, no matter how small, whereas according to the Tosafot in Avoda
Zara (20a) , it seems that in the case of a small loss, preference
must indeed be given to buying from a Jew.
Finally, you didn't ask re
- kashrut: you need to be extra careful with insects since the produce won't have been checked
- trumot and maasrot: you should ask a rav since you might need to take them without a blessing.