"Oeilett" is a term found in early vintage tatting patterns. As used in tatting, oeillet indicates a ring. Lace, in essence, is a hole surrounded by thread. Oeillet fits that definition perfectly. It is a small hole which is defined by a line of thread. In tatting patterns it may be found with the terms, dot (a small ring) or Josephine Knot/ring (a small ring of single stitches.)
"Oeillet"(pl. oeillets) used in other needle work mediums may mean a buttonhole, the eye of the needle, a belt hole, a grommet, or an eyelet. (It is also French for a carnation flower.)
In the Ladies' Column of the Bruce Herald, Volume VI, Issue 414, 17 April 1872, Page 3 appeared this pattern which uses the term oeillet interchangeably with the term loop. Notice also the use of the term "pearl" or "pearl loop" to mean a picot.
Another example: GOLDEN STARS IN TATTING AND CROCHET BY MLLE. RIEGO DE LA BRANCHARDIÈRE. 1861. THE WRISTBAND. The pattern begins at the bottom of page 6 and ends on page 7. A very poor illustration of this appears on the last page. A free download is available for this booklet at the Antique Pattern Library: http://www.georgiaseitz.com/public/riego/riego03goldenstarsintattingcrochet.pdf
To aid the tatter in understanding and working this pattern, the modern terms are added in parentheses following the antique term.
1st illet (RING)Fill the shuttle with the gold silk or twine and commence a loop (RING) , work 2 double stitches, then (1 pearl (PICOT) and 2 double 3 times), draw the loop (RING) quite close; and for the
2nd illet (RING)Commence a loop (RING) half an inch from the last and work 2 double, then join to the last pearl loop (PICOT), work 2 double, 1 pearl (PICOT), 2 double, 1 pearl (PICOT), 2 double, draw close. Join to the Silk (THREAD)left between the illets (RINGS), which will keep it firm; and there will now be about a quarter of an inch between the illets (RINGS), which is just sufficient to keep the work straight, Repeat the 2nd illet (RING) until there are 21, then leave a quarter of an inch of silk (THREAD) and join to the last pearl (PICOT), leave another quarter and join to the next pearl (PICOT), which is the centre one of the illet (RING). Turn the work (REVERSE WORK) and join to the centre pearl loop (PICOT) of each illet (RING), leaving a quarter of an inch between to make a straight line to correspond with the first side. Fasten off.