From Middle High German rouchen, röuchen, from Old High German rouhhen, from Proto-West Germanic *raukijan. By surface analysis, Rauch (“smoke”) + -en.
The form without umlaut is due to (chiefly Upper German) umlaut hindrance before velars and/or readaptation to the noun. Some dialects use either form throughout, others came to distinguish both forms (transitive vs. intransitive). In the latter case, the umlauted form usually took on the transitive use. In Modern Standard German, räuchen was displaced by the extended form räuchern (see there). The use for “to inhale tobacco” (later 17th c.) is a calque of French fumer.
rauchen (weak, third-person singular present raucht, past tense rauchte, past participle geraucht, auxiliary haben)
| infinitive | rauchen | ||||
|---|---|---|---|---|---|
| present participle | rauchend | ||||
| past participle | geraucht | ||||
| auxiliary | haben | ||||
| indicative | subjunctive | ||||
| singular | plural | singular | plural | ||
| present | ich rauche | wir rauchen | i | ich rauche | wir rauchen |
| du rauchst | ihr raucht | du rauchest | ihr rauchet | ||
| er raucht | sie rauchen | er rauche | sie rauchen | ||
| preterite | ich rauchte | wir rauchten | ii | ich rauchte1 | wir rauchten1 |
| du rauchtest | ihr rauchtet | du rauchtest1 | ihr rauchtet1 | ||
| er rauchte | sie rauchten | er rauchte1 | sie rauchten1 | ||
| imperative | rauch (du) rauche (du) |
raucht (ihr) | |||
1Rare except in very formal contexts; alternative in würde normally preferred.