You can probably skip "design office" since it is covered by "designing" (depending on how it is worked into your French text).

Here's an example of where "designing draftsman" fits into the scheme of things:

Mr. Armstrong pioneered in the design and construction of electrical transmission towers throughout California. He began his career in 1905 as an assistant in chemical laboratories in Ohio and West Virginia. FROM 1906 TO 1913, HE WORKED AS A DRAFTSMAN for various firms in West Virginia, Illinois, Ohio, Indiana, and Pennsylvania. From 1913 TO 1918, HE WAS ASSISTANT IN THE BRIDGE DEPARTMENT of the Pennsylvania Lines West of Pittsburg, PA. He joined the Power Construction Company in San Francisco, CA, IN 1918, AND THE GREAT WESTERN POWER COMPANY IN 1921, AS DESIGNING DRAFTSMAN. In 1922, HE BECAME DESIGNING ENGINEER in full charge of engineering work for the Pacific Coast Steel Company tower department and in 1927 until he retired in 1930, he was CHIEF ENGINEER OF THE TOWER DEPARTMENT
http://cedb.asce.org/cgi/WWWdisplay.cgi?6599901

Material Supplied To DESIGNING DRAFTSMAN
In any electric machine, the design must be an intermingling of electrical and mechanical features. The designing engineer usually gives more of the mechanical details than in some other classes of machinery because these details affect the electrical features. Practice varies in every manufacturing plant to some extent in this respect. Thus, in one place the engineer may go so far as to determine the size of the shaft necessary, while in another the CALCULATION OF SOME OF THE ELECTRICAL FEATURES MAY BE LEFT TO THE DESIGNING DRAFTSMAN.
In general, the DESIGNING DRAFTSMAN is supplied with complete tables of the electrical features giving all details of the various windings, the length or size of the magnetic circuits, and the material to be used for them, together with any other features of design which must be followed in order to meet the requirements. The electrical features may be given in the form of tables which may give all necessary data as to size and number of conductors in fields and armature, the size and arrangement of slots in the armature laminations, and the kind of insulation and its arrangement. From this data the draftsman must make his drawings complete in every detail, so that the machine can be built in the shops.
http://chestofbooks.com/crafts/machinery/Shop-Practice-V2/De...

I think in the following "draftsman" is to be understood "designing draftsman" in each case:
14. It is acceptable practice in the engineering community for an engineer to work with a designer who drafts design documents and is independently employed. It is also acceptable practice in the engineering community for an engineer working with a DESIGNING DRAFTSMAN not to visit a particular project site if sufficient detail of the project is related to the engineer by the draftsman.
15. It is acceptable practice in the engineering community for a draftsman to design complete drawings and then present the drawings to an engineer for engineering review and approval as long as the draftsman is known to the engineer and the engineer is aware of the draftsman’s skill and expertise.
http://www.5dca.org/Opinions/Opin2007/021207/5D06-2267.op.pd...

Mr. Adams was employed as a DRAFTSMAN by the Whatcom County (Washington) engineer’s office; then by the Bellingham Coal Company; and from January to August, 1921, served as DRAFTSMAN for the Barahona Company in Barahona, the Dominican Republic, on the design and construction of various irrigation facilities. From August 1920 to January 1921 and from October 1921 to July 1929, he was with the Department of Public Works of the Dominican Republic, first as a STRUCTURAL DRAFTSMAN; then, from October 1921 to January 1925 as ASSISTANT ENGINEER in charge of design of all bridges, public buildings, marine structures, and of construction, maintenance, and repair of these near Capitol City; and after January 1925 as engineer and, subsequently, as CHIEF OF THE ENGINEERING OFFICE in charge of structural design and maintenance as well as investigation and reports of sewage systems waterworks and on the operation of the Government Railroad. Mr. Adams was DESIGNING DRAFTSMAN with the Department of Highways and Public Works at Nashville, TN, from April 1930 to January 1931. In January 1933, he returned to the Whatcom County engineer’s office as DRAFTSMAN, and later, as CHIEF DRAFTSMAN on the design and construction of county roads, bridges, and irrigation works. From January 1936 to March 1938, Mr. Adams served as WATER SUPERINTENDENT AND CITY ENGINEER of Bellingham, WA, and in 1938 became ENGINEER INSPECTOR, PWA Region 7 and 6. Mr. Adams was CONSULTING ENGINEER on water systems improvement and maintenance for the Water Commission of Pendleton, OR, from October 1939 to June 1941, when he became CONSTRUCTION ENGINEER, PWA Region 7, in Seattle, WA. After 1949, he acted as SENIOR REVIEW ENGINEER in the Alaska Public Works Bureau of Community Facilities in the Housing and Home Finance Adminsitration in Juneau, AK. From 1954 until his retirement in 1957, Mr. Adams served as engineer for the Corps of Engineers in the Seattle District of the Alaska Section.
http://cedb.asce.org/cgi/WWWdisplay.cgi?6699901