Here's the thing about true French tarragon: it doesn't come true from seed, so don't waste your time with any packet labeled 'tarragon' — that's almost always the inferior Russian tarragon, which is coarse and nearly flavorless. Start with a plant from a reputable nursery, or beg a division off a gardening friend in spring. It hates wet feet more than almost anything, so the single biggest mistake is planting it in heavy clay that stays soggy — work in plenty of grit or coarse sand first and give it a spot that drains fast. Set it out after your last frost in a sunny, sheltered bed. It's hardy down to zone 4 but appreciates a light winter mulch in the colder end of its range. Every three or four years the plant gets woody and the flavor fades, so divide it in early spring to keep it vigorous; that's also your free supply of new plants. Pinch out the flower buds when they appear — they sap energy and the leaves are what you're after anyway.
French tarragon is one of the great culinary herbs, the soul of a proper béarnaise sauce and the classic partner to chicken, eggs, and fish. That gentle anise-licorice note is best fresh, since drying flattens it badly; instead, snip sprigs through the season and steep them in white wine vinegar for a tarragon vinegar that keeps the flavor all winter, or freeze chopped leaves in oil. Traditionally the plant earned the name 'dracunculus,' little dragon, from its serpentine roots, and herbalists once chewed the leaves to numb toothache and ease digestion — the mild numbing tingle on your tongue is real and tells you you've got the genuine article. It was also used as a mild appetite stimulant and digestive tonic, taken as a simple infusion after heavy meals.
Powdery mildew
White or grey powdery coating on leaves — usually starting on older growth in humid conditions or when nights cool.
Improve air circulation by thinning plants. Apply neem oil or potassium bicarbonate spray at first sign. Avoid overhead watering.
Rust
Orange to brown raised pustules on the undersides of leaves, with yellow spotting on the upper surface. Heavy infections cause leaves to yellow and drop.
Remove and destroy infected leaves. Avoid overhead watering and improve air circulation. Apply a sulfur or copper-based fungicide if it spreads. Clear plant debris in fall.
Crown Rot
Lower leaves yellow and wilt; the base of the rosette turns brown and soft, sometimes with white fungal threads at the soil line. Plants collapse in wet conditions.
Remove and destroy affected plants. Improve drainage and avoid overhead watering. Do not mulch directly against the crown. Space plants for airflow and avoid replanting in the same wet spot.
Downy mildew
Yellowing on top of leaves with grey-purple fuzz underneath. Spreads rapidly in humid conditions.
Remove affected leaves. Improve air circulation. Avoid overhead watering. Copper spray as preventive.
Spider Mites
Tetranychus urticae →Fine stippling or bronzing on leaves, faint webbing on undersides, foliage drying out during hot, dry weather.
Spray foliage with a strong jet of water to dislodge mites. Apply insecticidal soap or horticultural oil to leaf undersides; repeat every 5–7 days as needed.