A proper answer will depend on whether a IRTF has also been issued
This may depend on the exact French wording (which I cannot read), but the Google Translated text implies a can and not a will.
The The obligation to leave French territory (OQTF) does not directly state under what conditions you may return to France after fulfilling the OQTF order without a IRTF order.
It does imply that a OQTF can be issued togeather with a IRTF, which then such a ban on reentry would apply.
There is no indication that the OQTF is stamped into the passport, so without a IRTF order, a reentry would depend on the information contained in the Passport itself.
If an unexpired residence permit exists, then formaly, you may reenter. Once the permit has expired, then formaly, the 90/180 days rule would start.
If you undertake a border hopping activity between the Schengen Area and the United Kingdom, then assume that at some point the Border Guards of both may start to ask questions. The combination of expired permit and border hopping will leave a telling trail.
So a Schengen Area border guard may not let you back in.
If they do a thorough check and the OQTF order is found, an IRTF may be issued. The Schengen Information System (SIS) will then contain an entry about your activity.
If the Entry/Exit System (EES) comes into effect in 2020/21, the SIS will be checked as part of the enter/exit process.
The Prohibition of return on French territory (IRTF) also does not explicitly state that a IRTF is always issued togeather with a OQTF with a voluntary withdrawal period.
It does state, that when issued, it effects future entry into the Schengen Area.
A automatic repeal of the IRTF seems to be possible after 2 months when
- you have left on time (exit stamp in passport)
- you present yourself to a french consulate
Voluntary departure within 30 days
End of 30 days
At the end of the 30-day period, you must have left France by your own means.
If you are still in France after this period, you can be placed in a detention center or under house arrest . The prefect informs you of a ban on returning to France (IRTF).
OQTF with voluntary withdrawal period
The IRTF can be pronounced after an OQTF (with 30 days voluntary departure period), if you stayed in France.
Duration of the prohibition
The IRTF lasts 2 years maximum from the execution of the OQTF.
Note: if you stayed in France despite the OQTF, you have a FTIR of 2 years which can be extended by up to 2 years.
The IRTF forbids you not only to return to France, but also to any country in the Schengen area.
Indeed, an IRTF pronounced in France leads to a report for the purposes of non-admission into the Schengen Information System (SIS) . You must be informed of your registration in this file when notifying the IRTF. This registration will prevent you from obtaining a visa to enter and stay in the Schengen area.
Cancellation of the return ban
The IRTF is repealed:
- if you left France within the time limit,
- and that you prove your exit in the 2 months following the expiry of this delay (the proof can be brought by the stamp affixed on your passport by the police at the borders or by any means, in particular by presenting yourself personally to the embassy or to the French consulate or to the Ofii delegation in the country of return).
If you return to France during the duration of the IRTF, you can be sentenced by the criminal judge:
- to a prison term of up to 3 years,
- and possibly a ban on French territory (ITF) .
Sources: (in French)