Thank you for such an interesting question.  Goosefoot, according to my research, is a garden weed that is said to have medicinal uses.  There are many weeds with similar pedigrees.  My best guess is that a 'goosefoot" herb garden would contain many plants that might be used for medicine or flavor.  If you are able to expose your stone pattern, it would be wonderful to use it as your base.  From what I can tell from your picture, that would be a lot of work.  If I were beginning such a task, I would start small, just one bed. I would use a raised bed built up from your foundation stones.   Deciding which plants to use would take some research.  You might get inspiration from famous gardens like Jefferson's at Montecello.  I have included an article about such an effort by a garden club.  This was designed and maintained by the club for another historical society.  I hope this provides inspiration for your project.  West Newbury is in Massachusetts.  This project was undertaken in 1966.

West Newbury - Hills House Herb Garden A West Newbury Garden Club project is the Goose-foot Herb Garden in front of the little old shoe-maker’s shop on the grounds of the Morse-Hills House, home of the West Newbury Historical Society. This appealing small garden, all green and fragrant, gay with the yellow and orange blossoms of calendulas, and “not a weed in sight” was one of the highlights of an Open House tour sponsored by the West Newbury Historical Society. Many were the sincere compliments expressed by Garden Club members who came from great distances to see it, and West Newbury Garden Club members had reason to be proud of their herb garden. Research, Foundation Preparations, and Partial Planting It all began several years ago when the President of the West Newbury Garden Club spoke of the great surge of interest in the Garden Clubs in herb gardening. She thought it would be a worthwhile project for our club to undertake an intensive study of herbs, their habits, and their uses. The members were very enthusiastic, a committee was formed, and a serious study on herbs was undertaken. It was decided to use Rosetta E. Clark son’s book “Herbs and Their Culture and Uses” as a guide. The club purchased the book and later presented it to the West Newbury Public Library. The book as divided into sections so that a member could present a review at each meeting throughout the year. Sometimes the program that followed were related to the current book review. Following one review on Propagation of Herbs, Mr. Roger Coggeshall, President of Cherry Hill Nurseries, lectured on “Propagation”, with an extensive exhibit of specimens and methods. In further research, members went on a pilgrimage to the home of Mrs. Bertha Whiting of Newburyport to see the herbs in her garden. Another program, the guest speaker, Miss Harrieta Jackman, presented a lecture on herbs, and members made a delightful arrangement featuring herbs. The interest on the subject of herbs continued with members studying independently various books on herbs, reading magazine articles, and collecting recipes, and it was decided to put some of this newly acquired knowledge to use. The next meeting a delicious herb luncheon of hot casseroles, biscuits, bread, salads and desserts, all containing herbs, was enjoyed by members and a few friends. Herb recipes were discussed after the luncheon and hints on herb gardening were exchanged. An exhibit of herb books on gardening and cooking was on display, with interesting herb wheels and charts showing medicinal uses of herbs, and the use of herbs in dyeing. Some of the books were: “Herbs, Their Culture and Uses” by Louise Evans Hale: “Magic in Herbs” by Leonie de Sounin; “The Art of Cooking with Herbs and Spices” by Milo Miloradovich; and “The Shaker Cook Book” by Caroline B. Piercy.