No native speaker but I give a try. See here:

https://fr.wiktionary.org/wiki/s%E2%80%99en_venir

Your French friend is right. It is considered obsolete in France but it is still in use in Canada.

Another source indicates that it has a literary usage:

https://www.larousse.fr/dictionnaires/francais/s_en_venir/81410

There is also a nice thread (in English) here:

https://forum.wordreference.com/threads/sen-venir-venir.1143808/

To the best of my understanding, I would translate it

Il s’en vient=> He is coming (from there).

That is en is a pronoun that can be translated from there. Like

J’y vais=>I’m going (there).

and

Je m’en vais=>I’m off / I’m leaving (from here).

It is impossible to gain an appreciable undertanding of the nuance sought without poring over a copious supply of examples from the literature. As your knowledge of French is inexistant, this is a serious drawback in your striving towards acquiring some notions on this point, which after all might only be a point of detail. Nevertheless, I would find it regrettable not to mention the few examples I can gather and in doing so to deprive the general reader of as wide a basis as possible for his/her assessment of the claims I’ll make; as I can’t take the time for a careful translation, I can only hope that a possible prolonged interest in elucidating this point will have you return to these sentences when made aware of a means to obtain a translation. I think that the very general terms used in characterising the nuance are justified as the nuance is not really a single entity but rather several, although each one is to be traced back to the general designation given. I do not claim, though, to be able to make out clearly a connection for all the examples given.

1. Votre Altesse donc quitte Ferrare et s’en vient secrètement à Venise, presque sans suite, affublée d’un faux nom napolitain, et alors que moi je l’étais d’un faux nom espagnol. (V. HUGO, Lucrèce Borgia, 1833, I, 2, p. 27).

2. Un froid avant-coureur s’en vient nous annoncer Que le chaud de la fièvre aux membres va passer. (LA FONTAINE, Le Quinquina, éd. H. Regnier, VI, p. 330)

3. Avec son chant calmeur qui soulage les âmes (…) La mer s’en vient mourir en rythmes cadencés (H. DE RÉGNIER, Premiers poèmes, Apaisement, 1886, p. 88).

4. Et la petite Primaverile s’en vient à nous, capricante, menue, les yeux luisants comme deux gouttes de café.

5. Le Christ crucifère, qui s’en vient vers toi (CLAUDEL, Corona Benignitatis, 1915, p. 407).

6. … avec dix chevaliers d’un sang très noble issus, Don Fadrique s’en vient de Coïmbre à Séville. Le jeune Maître, né de Doña Léonor, sur sa mule à grelots précède l’équipée, … (Doña.)

7. Partout l’automne est mélancolique, chargé du regret de ce qui s’en va et de la menace de ce qui s’en vient; mais sur le sol canadien, il est plus mélancolique et plus émouvant qu’ailleurs, et pareil à la mort d’un être humain que les dieux rappellent trop tôt…

8. Tout là-bas sur le Rhin s’en vient une nacelle Et mon amant s’y tient il m’a vue il m’appelle (APOLL., Alcools, 1913, p.116).

9. Tiens, il s’en vient me quêter (Canada 1930).

10. La lumière qui se filtre par la verdure tendre des marronniers s’en vient voluter autour de ses formes que la marche ondule. (MORÉAS, Le Thé chez Miranda, 1886, p. 17 ds RHEIMS 1969)

The “self propelled” aspect of displacement, as characteristic in the meaning of “vient” has to do with the relative wilfulness or rather amount of willpower, decisiveness and deliberateness found as a prime mover in the entity’s conscience as an explanation and a characteristic of how the displacement is brought about. By opposition the “motion due to external agency” aspect has to do with a relative absence of those qualities either as a consequence of the entity’s nature, which is a human creature at times but also often enough not a creature and typically a physical phenomenon that evolves over a short enough period of time. For this reason the cases collected above as pertain to “s’en vient” concern either beings whose maturity is far from having come to the full, human beings that do not act in a deliberate manner, or physical phenomena endowed with the characteristic of having a dynamic nature and things the nature of which is by definition associated with displacement (stars, ships, clouds, herds of cattle, patches of vegetation, etc.) ; in the examples we find the sensation of cold, the sea, the changes brought by the autumn, a frail craft, the light,…

As relating to small children the term “willy-nilly” is one of the those to associate with this idea and here is an example of mine to help drive this notion home;

The little girl went willy nilly from her father to her mother, her gaze arrested by turns on this and that as she tottered along. (One can’t be quite sure there is a sense of purpose in the child’s mind.)

Let’s see what can be said of that poem, « Le Facteur » ; « Il s’en vient, d’un pas régulier, » is meant to confer, it could be said, that in his routine, daily action the postman seems to be led by the ever same path used daily rather than to be moving along it in a deliberate manner.