Compromittere, Compromise, Compromit
In Late Middle English there are two sets of words ultimately derived from Medieval Latin compromittere, ‘to make a mutual promise’: (1) through Old French compromis the identical noun and the derived verb compromisen, (2) and the verb compromitten directly from the Latin. As commission is a nominal derivative of commit, compromission derives from compromit.
No negative connotations emerge for compromise until the early 17th c.; for compromit/compromission not until the late 18th, and only in an emergent US English, particularly among political elites.
This raises the intriquing possibility that French influenced American usage of compromit/compromission, but not across the Channel. According to the Dictionnaire de l’Académie Française (9th ed.), the word compromission did not take on the meaning you cite until the 18th c., a time when Benjamin Franklin, Thomas Jefferson et al. sojourned in Paris hoping to solicit French aid against the British.
Until then, the meanings of compromise and compromit were virtually identical — the main reason why the latter eventually disappeared, even in America. Both describe the act of coming to a mutual agreement in a sense modern speakers would recognize, but also submitting an issue to arbitration (“put in/to compromise,” “compromise to/unto” an arbitrator), a meaning still current in the 19th c. but no longer. Compromit, however, could be used reflexively, as in to pledge oneself to take a course of action.
The seide abbot shall haue and enioye the seide londes … with all the issues and profites that have bene take therof seth [since] the day of compromyssion. — Cartularium Monasterii Sancti Johannis Baptiste de Colecestria, 1430.
In a Cathedrallkurk of Fraunce þer fell a dis-corde for chesyng of þer bisshopp. So þai compromysid vnto a cardinall … þat he sulde chese þaim one of ij  whame þai namyd. — Alphabet of Tales, ca. 1450.
Both parties consentid that þe compromisse i-maade togedur … bytwene þem … be i-cancellid. — The English Register of Oseney Abbey, by Oxford, ca. 1460.
The same parties have compromitted tham self to abide the arbitrement of and upon þe premisses. — The Stonor Letters and Papers, 1475.
Ther hath longe honged a mater yn travers betwene my lord the Bysshop..and the Maier and the Comminalte of the Cite of Excetre, whiche by the kyngs commaundement was putte yn compremys and rule of my lord Chaunceller. — The Shillingford Letters and Papers, 1448.
Put to Compromise
As in Middle English, in the 17th c. put to compromise could still mean ‘submit to arbitration’:
[Captain Bonville]… you are as afraid of a torn suit, as a younger brother of a sergeant, a rich corn-master of a plentiful year, or a troublesome attorney to hear of suits put to compromise. — Thomas Heywood, The Royal King and Loyal Subject (performed c. 1615-18; printed 1637), ed., John P. Collier, 1853.
Influenced by the French mettre en compromis, however, in the early 17th c. the corresponding English idiom takes on the negative meaning of either ‘exposed to hazard, danger’ or the equally modern sense of compromising one’s honor, reputation, etc. This meaning accrued to compromise alone in the 1690s.
… the duke of berry making the like request for him, in the presence of the children of the duke of orleans, melting with teares, weeping with sobs, to see the bloud of their father put to compromise, and themselues forced to forget so sencible an iniurie: — Edward Grimstone, trans., Pierre Matthieu, The History of Levvis the Eleuenth, 1614. EEBO
… it was not thought conuenient, that the patriarch should with his person put the reputation of the Holie see to compromise: — Edward Grimstone, trans., Pierre d’Avity, sieur de Montmartin, The estates, empires, & principallities of the world, 1615. EEBO
this was contradicted by many of the catholiques, who thought it strange, dishonourable, and dangerous to put the religion of their predecessours, receiued vntill that time, to compromise, and in hazard: — Nathaniel Brent, trans., Paoli Sarpi, The Historie of the Councel of Trent, 1629. EEBO
The Pope ill reliſhed this Propoſal, declaring that he would never conſent to have his Authority put to compromiſe, or his Power compounded for. — Paul Rycaut, trans., Bartolomeo Platina, The Lives of the Popes, 1685.
Compromit, Compromission in American English
Influenced by the new French meaning of compromission, late 18th–19th c. American sources, but not British, use both verb and derived noun in a negative sense:
His [Barkley’s] affairs, too, are so embarrassed and desperate, that the public reputation is, every moment, in danger of being compromitted with him. — Thomas Jefferson, Letter to Dumas, Paris, 14 June 1787.
I should feel the more hesitation in adopting the opinions which I express in this case, were I not firmly convinced that they are practical, and may be acted upon without compromitting the harmony of the union, or bringing humility upon the state tribunals. — Assoc. Justice William Johnson, concurring opinion, Fairfax v. Hunter’s Lessee, Supreme Court of the US, 20 March 1816.
That to have given the agent the instructions which he says he did, “to investigate the plots, going on to enter into conferences (for which he had sufficient credentials) with the governors, and all other officers, civil and military, and, with their aid, to do on the spot whatever should be necessary to discover the designs of the conspirators—arrest them—bring their persons to punishment—and to call out the force of the country to suppress their proceedings” was to have exceeded all constitutional authority as president, if to be executed by the power of the United States; but if by state authority, then a compromission of his duty as president. — Humphrey Marshall, The History of Kentucky, 1824.
We are no advocate for war, but there are times when forbearance becomes a crime, and we hold that no greater curse can befall a people than a compromission of national esteem or national honor. — Boon's Lick Times (Fayette MO), 30 Jan. 1841.
In many cases of disease occurring in the very young and in the very old, mucus may so accumulate in the lungs, owing to the inability of the enfeebled powers to force it up, as seriously to embarrass, or even fatally compromit, respiration. — Horatio Curtis Wood, A Treatise on Therapeutics, Philadelphia, 1874.
At the same time, Andrew Jackson is comfortable using compromise in discussing the “war” between Michigan and Ohio over Toledo:
Without compromising the interest or honor of either Ohio or Michigan, I do not despair of at least a temporary accommodation of the unfortunate controversy existing between them. — Andrew Jackson, “Message from the President of the United States,” 1835.
Ohio got Toledo and Michigan the Upper Peninsula. As for compromit/compromission, the supplement to Webster’s Dictionary (1907) notes that all uses of compromission were obsolete except as a means of election by a small number of delegates to whom, in the older sense, the matter was compromised.
A lexical gap can only be shown to exist once it’s filled, say, by the absence of a distinct second person plural pronoun countered by informal British you lot or Southern US y’all. The French compromission entered American English, but died out in favor of compromise by the beginning of the 20th c. British English retained the same meaning of compromission it had in the 15th c. until it disappeared from common speech there as well. That 18th c. speakers of French made a distinction between compromis and compromission doesn’t mean that English speakers would do the same or that when they did, the word would remain current.
French influence did, however, enter into the history of compromise/compromit at three important junctures: in Late Middle English when compromise was first borrowed from Old French, from mettre en compromis in the 17th c. and compromission for a little over a century of American English.