How would you say that your "stomach twists" because of great surprise, shock, etc. ?
Can you say: "mon estomac se tord" ?
Une expression assez idiomatique qui se réfère aussi à l'estomac serait :
Avoir l'estomac retourné
J'en ai l'estomac tout retourné !
avoir l'estomac noué
Une autre expression liée à l'estomac. Cela signifie être anxieux, se sentir mal au point d'en sentir une gêne.
Ces examens me stressent tellement, j'en ai l'estomac noué / des nœuds à l'estomac.
No, an imaginative French speaker might guess at what you are trying to say but this combination of words is not at all used to express that someone has butterflies in the stomach.
It's an open question whether various emotions are the cause of the same physiological reactions in our bodies at all times and whatever the ethnicity we belong to. Moreover, it is clear that man has for a long time associated bodily organs with various mental states in a very approximate fashion.
In the case of very strong emotion, such as caused by horribly sickening situations, some people may be affected to the point of vomiting; there is no doubt that "twisting" of the stomach is a preliminary and that the stomach is affected to a greater or a lesser extent. In French the expression "avoir l'estomac retourné" is used for this type of emotion that has to do with sickening situations but that is all. In fact it is used also for stomach troubles caused by the ingestion of food that is not fit for eating and it is used also for nausea-like sickness.
Apparently, the French identify more readily the throat as the physiological recipient of mental schock: the sudden death of a husband, of a child… Those are shocks which those that bear their impact make manifest by saying that "ils/elles ont la gorge serrée", "ils/elles ont senti leur gorge se serrer". The heart is also believed to be one of the seats of the manifestation of physical sensations due to intense emotion like fear, especially sudden fear, and like great sadness. In this case too we find expressions such as "le cœur se serre" (voir ce poème), "son cœur se serra", "avoir le cœur serré".
The expression "glacer le cœur" is used to communicate the effect that great fear or great horror produces;
Further research instigated by @Lyzvaleska shows that "glacer le sang is more common in french; it is found in the TLFi whereas "glacer le cœur" is not.
The following are found in the TLFi;
Congeler le sang, le cœur, le cerveau. Inhiber les réactions, rendre incapable de fonctionner normalement (ce qui est assimilé métaphoriquement ou non à un fluide) :
However, the physiological reactions that are related in those expressions are apparently of a type brought about by physical conditions, not by emotional stress.